Article
Mathematics
Haiyan Li, Bo Wang
Summary: This paper focuses on the incompressible 2D stochastic Navier-Stokes equations with linear damping. By utilizing new calculation estimates, the existence of random attractor and the upper semicontinuity of the random attractors as epsilon -> 0(+) in the two-dimensional space are proven.
Article
Mathematics
Flank D. M. Bezerra, Marcelo J. D. Nascimento
Summary: This article focuses on the long-time dynamics of a class of semilinear thermoelastic systems with variable thermal coefficient. The main results establish the existence, regularity, and upper semicontinuity of the pullback attractors with respect to the coefficients of thermal expansion of the material under nonlinear forces and suitable conditions of growth and dissipativity.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Mirelson M. Freitas, Anderson J. A. Ramos, Mauro L. Santos
Summary: This paper focuses on studying the asymptotic behavior of a binary mixture problem of solids with fractional damping and sources terms. The existence of global attractors with finite fractal dimension and exponential attractors is proven. Additionally, the upper-semicontinuity of global attractors as the fractional exponent tends to zero is also established.
APPLIED MATHEMATICS AND OPTIMIZATION
(2021)
Article
Mathematics, Applied
Na Lei, Shengfan Zhou
Summary: This paper investigates the attractors and their upper semicontinuity of second and first order nonautonomous lattice systems with singular perturbations, proving convergence under certain conditions and the embedding relationship when perturbation disappears. Additionally, the existence and exponential attraction of singleton pullback attractors for the systems are considered.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2022)
Article
Mathematics, Applied
Moncef Aouadi, Souad Guerine
Summary: In this paper, we investigate the long-time dynamics of pullback attractors for a non-autonomous and nonlinear full von Karman beam, as well as its upper semicontinuity property. The one-dimensional full von Karman beam equations are a fundamental model for describing the nonlinear oscillations with large displacements. By assuming general conditions on nonlinear damping and source terms, and using nonlinear semigroups and the theory of monotone operators, we establish the existence and uniqueness of weak and strong solutions. We also prove the existence of pullback attractors in the natural space energy, and demonstrate the regularity of the family of pullback attractors and its upper semicontinuity with respect to non-autonomous perturbations.
ACTA APPLICANDAE MATHEMATICAE
(2023)
Article
Mathematics, Applied
Yanxia Qu, Zhijian Yang
Summary: This paper establishes the upper semicontinuity of the strong global attractors A(0) on the dissipative index for the Kirchhoff wave model with structural nonlinear damping, extending previous research on the topic. The result presented in this study improves and deepens those found in recent literature, enhancing our understanding of strong attractors in such models.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Yongqiang Fu, Xiaoju Zhang
Summary: This paper investigates initial boundary value problems for the time-space fractional Rosenau equation, establishes decay estimates of weak solutions to corresponding linear equations, and proves the global existence and asymptotic behavior of weak solutions in time-weighted Sobolev spaces under small initial value conditions. Additionally, the regularity of weak solutions is discussed when initial value data are strengthened.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Maria Colombo, Silja Haffter
Summary: In this paper, we study the defocusing nonlinear wave equation in three dimensions. We prove the global well-posedness of the equation for any initial datum with a scaling-subcritical norm bounded by M0 at p = 5 + i, where i is from the interval (0, i0(M0)).
Article
Mathematics, Applied
Yongqin Xie, Jun Li, Kaixuan Zhu
Summary: This paper investigates the upper semicontinuity and regularity of attractors for nonclassical diffusion equations, extending the asymptotic a priori estimate method and utilizing a new operator decomposition method to obtain some extended and improved results. Furthermore, the regularity of global attractors is established, extending and improving upon previous findings.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
Yonghai Wang, Minhui Hu, Yuming Qin
Summary: This paper discusses the local uniformly upper semicontinuity of pullback attractors for a strongly damped wave equation. It proves that, under certain proper assumptions, the pullback attractor of the equation satisfies a specific condition.
BOUNDARY VALUE PROBLEMS
(2021)
Article
Mathematics
Vladimir Georgiev, Hideo Kubo
Summary: In this study, we investigate the Strauss conjecture for the 3D nonlinear wave equation with singular potential and provide a positive answer regarding its global existence. The main approach is to utilize the additional decay of the solution outside the light cone. By deriving appropriate conformal-type energy estimates, we prove the validity of this conjecture.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Stanislav Antontsev, Ivan Kuznetsov, Sergey Shmarev
Summary: In this paper, we study the Dirichlet problem for the pseudo-parabolic equation. Under appropriate conditions, it is shown that the problem has a global in time solution with certain properties. Sufficient conditions for uniqueness of the solution are derived for specific choices of the source, and the stability of the solutions with respect to perturbations of the nonlinear structure of the equation is proven. The rate of vanishing of llullW1,2(omega) is also found.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Joachim Krieger, Jonas Luhrmann, Gigliola Staffilani
Summary: We establish the global well-posedness of the energy-critical Maxwell-Klein-Gordon equation in the Coulomb gauge for scaling super-critical random initial data. The proof relies on an induction on frequency procedure and a modified linear-nonlinear decomposition based on a delicate probabilistic parametrix construction. This is the first result that guarantees the global existence of a geometric wave equation with random initial data at scaling super-critical regularity.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2023)
Article
Mathematics, Applied
Leonardo Pires
Summary: In this paper, the authors study Lipschitz perturbations of the Chafee-Infante equation, which is not differentiable. They prove the permanence and stability of equilibrium points and establish a Lipschitz version of the Hartman-Grobman theorem to find a local homeomorphism that maps orbits near each equilibrium point. The authors also demonstrate the continuity of attractors under Lipschitz perturbations.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Anna Kiesenhofer, Joachim Krieger
Summary: The study shows that the half-wave maps problem on R4+1 with target S-2 is globally well-posed for smooth initial data which are small in the critical l(1) based Besov space. This result serves as a formal analogue of the one proved by Tataru for wave maps.
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Jan W. Cholewa, Anibal Rodriguez-Bernal
Summary: This paper analyzes evolution problems associated with homogeneous operators and discusses the sharp estimate issues on homogeneous spaces and fractional power spaces. It also considers fractional diffusion problems and Schrodinger type problems, and applies these general results to a wide range of PDE problems.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2022)
Article
Mathematics, Applied
Tomas Caraballo, Alexandre N. Carvalho, Jose A. Langa, Alexandre N. Oliveira-Sousa
Summary: This work investigates the permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic perturbations, including the robustness and existence of exponential dichotomies for the linear case as well as the persistence of hyperbolic equilibria for nonlinear differential equations. The study demonstrates the existence of bounded random hyperbolic solutions for nonautonomous random dynamical systems perturbed by an autonomous semilinear problem and shows the convergence of these solutions to the autonomous equilibrium.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics
Ruben Caballero, Alexandre N. Carvalho, Pedro Marin-Rubio, Jose Valero
Summary: This paper investigates the structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation. It proves that the attractor consists of stationary points and their heteroclinic connections.
Article
Mathematics, Applied
Tomas Caraballo, Alexandre N. Carvalho, Jose A. Langa, Alexandre N. Oliveira-Sousa
Summary: In this paper, we study the stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove the robustness of nonuniform hyperbolicity for linear evolution processes and provide conditions for the uniqueness and continuous dependence of projections associated with nonuniform exponential dichotomies. An example of an evolution process in a Banach space that exhibits nonuniform exponential dichotomy is presented, and the permanence of nonuniform hyperbolicity under perturbations is studied. Finally, we prove the persistence of nonuniform hyperbolic solutions for nonlinear evolution processes under perturbations.
ASYMPTOTIC ANALYSIS
(2022)
Article
Mathematics
Hongyong Cui, Alexandre N. Carvalho, Arthur C. Cunha, Jose A. Langa
Summary: The paper aims to find an upper bound for the fractal dimension of uniform attractors in Banach spaces, utilizing a technique based on compact embedding of auxiliary Banach space into the phase space and corresponding smoothing effect. The bounds on fractal dimension are given in terms of symbol space dimension and Kolmogorov entropy number of the embedding. Applications show finite-dimensionality of attractors in specific equations and spaces.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
M. C. Bortolan, A. N. Carvalho, J. A. Langa, G. Raugel
Summary: This work investigates Morse-Smale semigroups under nonautonomous perturbations and introduces the concept of Morse-Smale evolution processes of hyperbolic type. The stability of the phase diagram of the attractors is proven, with intersecting stable and unstable manifolds. The complete proofs of local and global lambda-lemmas in the infinite-dimensional case, originally due to D. Henry, are included here for completeness.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Jan W. Cholewa, Anibal Rodriguez-Bernal
Summary: Motivated by previous analysis, this paper provides a spectral analysis of homogeneous operators and offers simple characterizations of generators of homogeneous semigroups and homogeneous sectorial operators. Homogeneous perturbations of homogeneous operators and semigroups are also analyzed. These results are utilized to study certain parabolic PDEs involving homogeneous operators, including fractional diffusion problems, and reveal a profound connection with Gagliardo-Nirenberg and Hardy type inequalities.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Alexandre N. Carvalho, Arthur C. Cunha, Jose A. Langa, James C. Robinson
Summary: We provide a simple proof of a result by Mane (1981) that states a compact subset A of a Banach space, which is negatively invariant under a map S, is finite-dimensional if DS(x) = C(x) + L(x) where C is compact and L is a contraction. Additionally, we demonstrate that if S is both compact and differentiable, A is finite-dimensional. Furthermore, we present some results concerning the (box-counting) dimension of such sets assuming a 'smoothing property' and the Kolmogorov epsilon-entropy of the embedding of Z into X. Finally, we apply these results to an abstract semilinear parabolic equation and the two-dimensional Navier-Stokes equations on a periodic domain.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Flank D. M. Bezerra, Alexandre N. Carvalho, Lucas A. Santos
Summary: In this paper, the well-posedness of the Cauchy problem associated with a third-order evolution equation is discussed. The equation involves mathematical concepts and conditions such as separable Hilbert space, unbounded sectorial operator, etc.
JOURNAL OF EVOLUTION EQUATIONS
(2022)
Article
Statistics & Probability
Tomas Caraballo, Jose A. Langa, Alexandre N. Carvalho, Alexandre N. Oliveira-Sousa
Summary: In this work, the continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems are studied. The existence and permanence of unstable sets of hyperbolic solutions are studied first, and then used to establish the lower semicontinuity of nonautonomous random attractors and the persistence of the gradient structure under nonautonomous random perturbations. The abstract results are applied to a stochastic differential equation and in a damped wave equation with a perturbation on the damping.
STOCHASTICS AND DYNAMICS
(2022)
Article
Mathematics, Applied
Alexandre N. Carvalho, Luciano R. N. Rocha, Jose A. Langa, Rafael Obaya
Summary: In this work, we investigate the structure of the skew-product attractor for a planar diffusively coupled ordinary differential equation. We provide a non-autonomous structure that completely describes the dynamics of this model and give a Morse decomposition for the skew-product attractor. Our findings indicate that the complexity of the isolated invariant sets is related to the complexity of the attractor, and when beta is asymptotically almost periodic, the isolated invariant sets will be almost periodic hyperbolic global solutions.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2023)
Article
Mathematics, Applied
Jakub Banaskiewicz, Alexandre N. Carvalho, Juan Garcia-Fuentes, Piotr Kalita
Summary: This paper studies the dynamics of slowly non-dissipative systems using the approach of unbounded attractors. It provides abstract results on the existence and properties of unbounded attractors, as well as the properties of unbounded omega-limit sets in slowly non-dissipative settings. The paper also develops the pullback non-autonomous counterpart of the unbounded attractor theory.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Jan W. Cholewa, Anibal Rodriguez-Bernal
Summary: We analyze the self-similarity properties of linear elliptic and evolutionary problems involving homogeneous operators in several spaces, including measures. Specifically, we employ these techniques to analyze 2mth-order diffusion equations and the associated fractional problems.
JOURNAL OF EVOLUTION EQUATIONS
(2023)
Article
Mathematics, Applied
Jan W. Cholewa, Anibal Rodriguez-Bernal
Summary: In this paper, the properties of linear higher-order parabolic equation in Morrey spaces are studied. The associated semigroup is proven to be analytic and sharp semigroup estimates in Morrey scale are obtained. The analysis also includes the study of semigroups in Morrey scale related to solving linear higher-order fractional diffusion equations.
ANALYSIS AND APPLICATIONS
(2023)
Article
Physics, Mathematical
Tomas Caraballo, Alexandre N. Carvalho, Heraclio Lopez-Lazaro
Summary: We present a global modification of the Ladyzhenskaya equations for incompressible non-Newtonian fluids. The modification involves a cut-off function and an additional artificial smoothing dissipation term, and aims at comparative analysis between the modified and non-modified systems. We demonstrate the existence and regularity of weak solutions, the existence of global attractors, the estimation of fractal dimension of global attractors, and the relationship of the autonomous dynamics between the modified and non-modified systems.
JOURNAL OF MATHEMATICAL PHYSICS
(2023)
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)