Article
Mathematics, Applied
Rasika Mahawattege, Roberto Triggiani
Summary: The study investigates a fluid-structure interaction model in a doughnut-like domain, with dynamic Stokes equations in the exterior sub-domain and an elastic structure in the interior sub-domain. A significant aspect is the inclusion of a strong viscoelastic damping term of Kelvin-Voigt type in the structure equation, impacting the boundary conditions at the interface and causing unbounded perturbations. Results show analyticity of the semigroup of contractions defining the coupled system, uniform exponential decay, and sharp spectral properties of its generator. Some results are dependent on the geometry.
APPLIED MATHEMATICS AND OPTIMIZATION
(2021)
Article
Mathematics, Applied
Jianan Cui, Shugen Chai
Summary: In this study, we analyze a Timoshenko system with partially Kelvin-Voigt damping and Cattaneo/Fourier type heat conduction. Previous research has shown non-exponential stability in Timoshenko systems with either heat conduction or partial Kelvin-Voigt damping alone. Here, we introduce Kelvin-Voigt damping into the thermoelastic Timoshenko system and prove that the system remains non-exponentially stable in cases of Fourier and Cattaneo type heat conduction, regardless of the wave speeds being equal or not. Furthermore, we demonstrate the optimal decay rate of the semigroup to be t-(c).
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Victor R. Cabanillas Zannini, Teofanes Quispe Mendez, Juan Sanchez Vargas
Summary: In this manuscript, the asymptotic behavior of two laminated beam systems is studied. The effect of different types of damping on the stability of the systems is analyzed, and the polynomial stability of each system is investigated.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Marcelo M. Cavalcanti, Valeria N. Domingos Cavalcanti, Dilberto da Silva Almeida Junior, Victor Hugo Gonzalez Martinez, Mauro de Lima Santos
Summary: In this manuscript, we analyze the exponential stability of a strongly coupled semilinear system of Klein-Gordon type with local dampings distributed around the boundary according to the geometric control condition. We show that the energy of the system exponentially decays to zero for all initial data in bounded sets of the finite energy phase space. We also prove the exponential decay for the linear problem associated with this system, without any restrictions on the space dimension or the initial data in the phase space.
ADVANCED NONLINEAR STUDIES
(2022)
Article
Mathematics, Applied
Kais Ammari, Farhat Shel, Louis Tebou
Summary: In this paper, we investigate the regularity of two damped abstract elastic systems, where the damping and coupling involve fractional powers of principal operators. By proving the analyticity of the underlying semigroup and the certain Gevrey classes for different parameter ranges, we analyze the characteristics of the systems and provide some application examples.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Victor Cabanillas Zannini, Leyter Potenciano-Machado, Teofanes Quispe Mendez
Summary: This paper uses semigroup theory to investigate the well-posedness and stability estimates of a delayed laminated beam system with Kelvin-Voigt damping. The results show exponential and polynomial stability, as well as optimal decay rates in the case of polynomial stability.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
C. A. Nonato, C. A. Raposo, B. Feng, A. J. A. Ramos
Summary: In this paper, a model of laminated beams with combined viscoelastic damping and strong time-delayed damping is considered. The global well-posedness is proved using the theory of semigroups of linear operators. It is shown that the lack of exponential stability occurs when the speed wave propagations are not equal, and the system polynomially approaches zero at a rate of t-1/2. On the other hand, with the equal-speed wave propagations, it is established that the energy decays exponentially.
ASYMPTOTIC ANALYSIS
(2023)
Article
Mathematics, Applied
Mouhammad Ghader, Rayan Nasser, Ali Wehbe
Summary: This paper investigates the stabilization of a one-dimensional wave equation with localized internal viscoelastic damping of Kelvin-Voigt type in a bounded domain. By using frequency domain arguments combined with the multiplier method, it is proven that the energy of the system decays optimally with type t(-4), considering only one damping Kelvin-Voigt mechanism acting inside the body.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Automation & Control Systems
Jun Liu, Weiping Yan, Can Zhang
Summary: This paper investigates the stabilizability of a quasilinear Klein-Gordon-wave system with variable coefficients in Rn. The stabilizability of linear wave-type equations with Kelvin-Voigt damping has been considered by Liu-Zhang and Yu-Han for different systems. In this paper, it is shown that there exists a linear feedback control law that can exponentially stabilize the quasilinear Klein-Gordon-wave system under certain smallness conditions, with the feedback control being a strong Kelvin-Voigt damping.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2023)
Article
Mathematics, Applied
Smain Moulay Khatir, Farhat Shel
Summary: The study investigates adding Kelvin-Voigt damping to a thermoelastic system to address delays, proving the well-posedness of the system using semigroup theory, and demonstrating the exponential stability of the system through the introduction of a suitable Lyapunov functional.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics
Hua-Lei Zhang
Summary: In this paper, the energy decay of a coupled wave system with local Kelvin-Voigt damping is studied. By using Carleman estimate and the frequency-domain method, it is shown that the energy of the system decays logarithmically when the damping coefficient function and the coupling coefficient function satisfy suitable assumptions.
MATHEMATISCHE NACHRICHTEN
(2023)
Article
Mathematics, Applied
Ali Wehbe, Mouhammad Ghader
Summary: This paper studies the indirect stability of Timoshenko system with local or global Kelvin-Voigt damping under various boundary conditions. The energy decay of the system is proven to follow a polynomial decay of type t(-1) and is considered optimal. The method employed combines frequency domain approach with multiplier method.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Ahmed Bchatnia, Karim El Mufti, Rania Yahia
Summary: Studying the dynamics of mixed elastic strings, it was shown that energy decays polynomially only when the lengths satisfy a certain condition.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Draifia Alaeddine
Summary: This work addresses decay rates for energy in a system of nonlinear singular viscoelastic equations with a nonlocal boundary condition. The study proves decay rates for the energy of a singular one-dimensional viscoelastic system with a nonlinear source term and nonlocal boundary condition.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Jianan Cui, Shugen Chai, Xiaomin Cao
Summary: In this paper, a 1-d Timoshenko-type system of thermoelasticity with local distributed Kelvin-Voigt damping is studied. The well-posedness and strong stability of the system are proved by combining semigroup theory with the principle of unique continuation. Furthermore, it is shown that the energy of the system decays polynomially with a decay rate of t-4 for 0 <= alpha < 1 using frequency domain arguments and piecewise multiplier techniques.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Anderson J. A. Ramos, Manoel J. Dos Santos, Mirelson M. Freitas, Dilberto S. Almeida Junior
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2020)
Review
Engineering, Mechanical
Anderson J. A. Ramos, Dilberto S. Almeida Junior, Alinia R. Santos, Edson A. Araujo, Pedro T. P. Aum
JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING
(2020)
Article
Mathematics
A. J. A. Ramos, D. S. Almeida Junior, L. G. R. Miranda
ARCHIV DER MATHEMATIK
(2020)
Article
Mechanics
D. S. Almeida Junior, A. J. A. Ramos, A. Soufyane, M. L. Cardoso, M. L. Santos
Article
Physics, Mathematical
M. J. Dos Santos, M. M. Freitas, A. J. A. Ramos, D. S. Almeida Junior, L. R. S. Rodrigues
JOURNAL OF MATHEMATICAL PHYSICS
(2020)
Article
Mathematics, Applied
A. J. A. Ramos, A. O. Ozer, M. M. Freitas, D. S. Almeida Junior, J. D. Martins
Summary: This paper investigates the effect of a delayed feedback on the overall exponential stabilizability dynamics of a piezoelectric beam, showing that the coefficient of the delayed feedback must be strictly less than the coefficient of the state feedback for exponential stability to be retained. The results are compared to the electrostatic case for further analysis.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2021)
Article
Mathematics, Applied
D. S. Almeida Junior, B. Feng, M. Afilal, A. Soufyane
Summary: The study focuses on the stabilization properties of dissipative Timoshenko systems, particularly on partially damped Timoshenko systems. Recent results highlight the significance of the second spectrum of frequency in the analysis of stabilization, showing its crucial role in the stability scenario of Timoshenko type systems.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2021)
Article
Mathematics, Applied
D. S. Almeida Junior, A. J. A. Ramos, M. M. Freitas
Summary: This paper investigates the relationship between the shear beam model and the classical Timoshenko beam model, demonstrating that the shear beam model exhibits energy exponential decay due to having only one finite wave speed.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
M. L. Santos, D. S. Almeida Junior, S. M. S. Cordeiro
Summary: In this paper, we investigate a one-dimensional porous-elastic system with nonlinear localized damping. By establishing an energy decay model and utilizing observability inequality, unique continuation property, and the reduction principle, we derive specific results that generalize and improve previous literature outcomes.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
A. J. A. Ramos, D. S. Almeida Junior, M. M. Freitas
Summary: In this paper, we study the porous-elastic equations with Kelvin-Voigt dissipation mechanisms and thermal effect given by Fourier's law. We show that the system lacks exponential decay property for a specific equality between damping parameters. In this direction, we prove polynomial decay and the optimal decay rate.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
D. S. Almeida Junior, M. M. Freitas, A. J. A. Ramos, A. Soufyane, M. L. Cardoso, A. D. S. Campelo
Summary: In this paper, we study the Timoshenko-Ehrenfest beam models and establish exponential decay results based on the influence of the second spectrum of frequency and its damaging consequences for wave propagation speeds. We prove the exponential decay property of the system and the exponential decay property of the total energy under different assumptions.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
D. S. Almeida Junior, A. J. A. Ramos, A. Soufyane, M. M. Freitas, M. L. Santos
Summary: This paper considers a one-dimensional coupled Timoshenko type system with a single weakly nonlinear feedback on the angular rotation. Without restrictive growth assumption on the damping term, an explicit and general decay rate is established using a multiplier method and properties of convex functions. This result improves earlier research by removing the need for the equal wave speeds assumption.
ACTA APPLICANDAE MATHEMATICAE
(2022)
Article
Mathematics
D. S. Almeida Junior, A. J. A. Ramos, E. L. M. Borges Filho
Summary: This work discusses the uniform observability of a semi-discrete Timoshenko beam model and establishes an observability inequality for a particular class of solutions given by Fourier's development. It is proven that there is a lack of numerical observability to the spectral problem in the setting of spatial finite difference, as the observability constant blows up as the mesh size tends to zero. The semi-discrete system in finite difference avoids the numerical anomaly of locking phenomenon and raises an important problem in theoretical numerical analysis regarding the determination of Fourier's solution considering the parity of vibration modes.
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO
(2022)
Article
Mathematics, Applied
Manoel J. Dos Santos, Baowei Feng, Dilberto S. Almeida Junior, Mauro L. Santos
Summary: This paper focuses on the existence of attractors for a nonlinear porous elastic system subjected to delay-type damping in the volume fraction equation. The study is conducted from the perspective of quasi-stability for infinite dimensional dynamical systems, leading to the results of global and exponential attractors.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2021)
Article
Mathematics
A. J. A. Ramos, M. Aouadi, D. S. Almeida Junior, M. M. Freitas, M. L. Araujo
Summary: In this work, a truncated version of the Timoshenko beam model with thermal and mass diffusion effects is analyzed. The existence, uniqueness, and exponential stability of the global solution of this model are proven without assuming the equal wave speeds condition.
ARCHIV DER MATHEMATIK
(2021)
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)
