Article
Mathematics, Applied
Bolys Sabitbek, Berikbol T. Torebek
Summary: In this study, we investigate a double nonlinear porous medium equation with a novel nonlinearity condition in a bounded domain. We introduce the blow-up solution for the problem under consideration with negative initial energy and construct invariant sets of solutions using a set of potential wells. We also analyze the global existence and asymptotic behavior of weak solutions, as well as the occurrence of blow-up phenomena within a finite time for the positive solution of the double nonlinear porous medium equation.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Applied
Van Duong Dinh
Summary: We revisit the finite time blow-up problem for the fourth-order Schrodinger equation with a specific nonlinearity, proving the existence of non-radial blow-up solutions with negative energy using localized virial estimates and spatial decay of the nonlinearity. This result is the first one dealing with non-radial blow-up solutions to the fourth-order Schrodinger equations.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Luca Vilasi, Youjun Wang
Summary: In this study, we investigate the blow-up behavior of ground states of the fractional Choquard equation as the exponent p(epsilon) approaches the upper critical growth regime. We prove that the ground state blows up in the sense of epsilon approaching zero.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics, Applied
Zhanwei Gou, Jincheng Shi
Summary: In this paper, the authors investigate a parabolic problem with nonlinear Neumann boundary conditions. They derive lower bounds for the blow-up time of the solution using a modified differential inequality in higher dimensional spaces. Under appropriate assumptions, they also provide an upper bound for the blow-up time.
Article
Mathematics, Applied
Jinmyong An, Roesong Jang, Jinmyong Kim
Summary: In this paper, the focusing inhomogeneous nonlinear Schrodinger equation with inverse-square potential is studied. The criteria for global existence and blow-up of solutions to the equation are established, and the global existence and blow-up of solutions with different data situations are investigated.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2023)
Article
Mathematics
Aynur Bulut, Benjamin Dodson
Summary: Global well-posedness and scattering results for the logarithmically energy-supercritical nonlinear wave equation are established under the assumption that the initial data satisfies a partial symmetry condition. These results generalize and extend previous work by Tao in the radially symmetric setting, utilizing techniques involving weighted versions of Morawetz and Strichartz estimates with weights adapted to partial symmetry assumptions. Additionally, a corresponding quantitative result for the energy-critical problem is established in an appendix.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2021)
Article
Mathematics, Applied
Feng Binhua, Ruipeng Chen, Jiayin Liu
Summary: This paper studies blow-up criteria and instability of normalized standing waves for the fractional Schrodinger-Choquard equation. The authors establish general blow-up criteria for non-radial solutions in both L-2- critical and L-2-supercritical cases, and show the existence of normalized standing waves. The study also investigates the strong instability of normalized standing waves, significantly improving earlier results.
ADVANCES IN NONLINEAR ANALYSIS
(2021)
Article
Mathematics, Applied
Liliane Maia, Benedetta Pellacci, Delia Schiera
Summary: Existence results for a class of Choquard equations with potentials are established. The potential has a limit at infinity and it is invariant under the action of a closed subgroup of linear isometries of R-N. The positive solution found will be invariant under the same action. Power nonlinearities with exponent greater or equal than two or less than two will be handled. Our results include the physical case.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Chao Shi
Summary: This paper studies the existence of stable standing waves for a type of nonlinear Schrödinger equation. By obtaining the best constant of a generalized Gagliardo-Nirenberg inequality and applying the concentration compactness principle, the existence and orbital stability of standing waves in the L-2-subcritical, L-2-critical, and L-2-supercritical cases are proven.
Article
Mathematics, Applied
Ruobing Bai, Bing Li
Summary: In this work, the concentration phenomenon of an inhomogeneous nonlinear Schrodinger equation was studied. It was proven that the solution blows up in finite time under certain conditions. These results are the first of their kind for the case when the initial data does not have finite variance and is non-radial. Furthermore, the first result for the infinite time blow-up rate was obtained.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2023)
Article
Mathematics
Hideo Takaoka
Summary: The study focused on the Cauchy problem of the mass critical nonlinear Schrodinger equation with derivative and a mass of 4 pi. Global well-posedness was proven in H-1 under certain conditions, and the limiting profile of blow up solutions with the critical 4 pi mass was obtained using the concentration compact principle as originally done by Kenig-Merle.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics
Linfei Shi, Wenguang Cheng, Jinjin Mao, Tianzhou Xu
Summary: This paper investigates a reaction-diffusion equation with a Caputo fractional derivative in time and boundary conditions. It first proves the existence and uniqueness of local solutions using the principle of contraction mapping. Two sufficient conditions for the blow-up of solutions in finite time are obtained under certain initial data conditions. The existence of global solutions is studied when the initial data is sufficiently small, and the long-time behavior of bounded solutions is analyzed.
Article
Mathematics, Applied
Quang-Minh Tran, Hong-Danh Pham
Summary: The paper discusses global existence and blow-up results for a class of fourth-order wave equations with nonlinear damping term and super linear source term. It provides information on the decay rate of the solution when the weak solution is global, and estimates the lower and upper bounds of the lifespan of the blow-up solution when the weak solution blows up in finite time. Additionally, a sufficient condition is established to obtain the global existence and general decay rate of weak solutions when an external vertical load term is included in the problem.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2021)
Article
Mathematics, Applied
Xuan Liu, Ting Zhang
Summary: We study the asymptotic behavior of the modified two-dimensional Schrodinger equation in the critical regime and prove global-in-time solution for any smooth initial datum of small size. We also provide pointwise decay estimates and large time asymptotic formulas for the solution.
Article
Mathematics, Applied
Yaning Li, Yuting Yang
Summary: In this article, the Cauchy problem for time-space fractional pseudo-parabolic equations is considered. The estimation of Lp - Lq for the solution operator is obtained, and the critical exponents of the problem are determined when u(0) is in Lq(RN). Furthermore, global existence of the mild solution is also obtained when u(0) is in Lp(RN) and Lq(RN) is sufficiently small.
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)