Article
Mathematics, Applied
Jacobo Baldonedo, Jose R. Fernandez, Antonio Magana, Ramon Quintanilla
Summary: We studied the behavior of solutions of the one-dimensional linear strain gradient porous elasticity system with different dissipative mechanisms. Exponential decay of solutions was observed in cases of viscosity and viscoporosity, while slow decay, controlled by at least t-1/2, was observed in cases of hyperviscosity and hyperviscoporosity. Surprisingly, the second mechanism seemed to be more efficient than the first one in pulling the solutions rapidly to zero. Numerical simulations were performed to demonstrate the energy decay behavior of the solutions.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
Article
Materials Science, Multidisciplinary
D. S. Almeida Junior, A. J. A. Ramos, M. M. Freitas, M. J. Dos Santos, T. El Arwadi
Summary: This paper examines a porous-elastic system where dissipation mechanisms impact both the elastic and porous structures. The one-dimensional porous-elastic system is defined on bounded domains in space, and polynomial stability is proven under specific relationships between damping parameters. The optimality of the rate of polynomial decay is also established.
MATHEMATICS AND MECHANICS OF SOLIDS
(2022)
Article
Mathematics, Applied
J. R. Fernandez, R. Quintanilla
Summary: This note examines a linear system of partial differential equations modeling a one-dimensional two-temperatures thermo-porous-elastic problem with microtemperatures. A new set of conditions is proposed to ensure the existence, uniqueness, and exponential decay of solutions, based on the theory of semigroups of linear operators. (C) 2020 Elsevier Ltd. All rights reserved.
APPLIED MATHEMATICS LETTERS
(2021)
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
A. Magana, R. Quintanilla
Summary: This study focuses on the behavior of solutions to porous-thermo-elastic problems over time, specifically when one variable is considered quasi-static. The analysis involves three different situations and utilizes both classical Fourier law and Green-Naghdi heat conduction models.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2021)
Article
Mathematics, Applied
Hualei Zhang, Qiong Zhang
Summary: In this paper, the stabilization of a one-dimensional system of type II thermoelasticity with voids is considered. Exponential stability is achieved by introducing two local dampings on the last two equations. The polynomial decay of the model is also studied with only one global damping on the heat equation of type II.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
Article
Materials Science, Multidisciplinary
A. J. A. Ramos, D. S. Almelda Junior, M. Aouadi, M. M. Freitas, R. C. Barbosa
Summary: In this paper, necessary and sufficient conditions for obtaining stability properties are provided for the one-dimensional Lord-Shulman thermoelastic theory with porosity subject to microtemperature but without temperature. The microtemperature conduction equations are governed by Cattaneo-Maxwell's law. A stability number ?(0) involving all coefficients of the system is introduced based on recent results, and it is proven that the exponential decay of the corresponding semigroup holds if and only if ?(0) = 0. Otherwise, it is shown that the system loses exponential stability and its solution decays polynomially with a rate equal to 1/vt.
MATHEMATICS AND MECHANICS OF SOLIDS
(2023)
Article
Mathematics, Applied
Hamza Zougheib, Toufic El Arwadi, Abdelaziz Soufyane
Summary: This paper analyzes the energy decay of the thermoelastic porous system using the dual-phase lag theory, considering the classical approach and the second spectrum approach. The well-posedness and exponential stability are achieved for the classical approach under equal wave speed conditions, while a polynomial decay is observed. On the other hand, the truncated system shows well-posedness and exponential stability without any assumptions on physical parameters.
STUDIES IN APPLIED MATHEMATICS
(2023)
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
M. L. S. Oliveira, E. S. Maciel, M. J. Dos Santos
Summary: This paper analyzes the porous elastic system with a viscoelastic dissipative mechanism of Kelvin-Voigt type and proves the conditions for the existence of an analytic semigroup associated with the model, as well as the optimality of the decay rate.
APPLICABLE ANALYSIS
(2022)
Article
Physics, Mathematical
A. J. A. Ramos, D. S. Almeida Junior, M. M. Freitas, A. S. Noe, M. J. Dos Santos
Summary: This article examines the swelling problem in porous elastic soils with fluid saturation, studies the well-posedness of the problem based on semigroup theory, proves the dissipative nature of the energy associated with the system, and establishes the exponential stability of the system. To ensure stability, both viscous damping and a time delay term on the first equation of the system are considered.
JOURNAL OF MATHEMATICAL PHYSICS
(2021)
Article
Mathematics
Zineb Nid, Abdelfeteh Fareh, Tijani A. Apalara
Summary: This paper focuses on the well-posedness and asymptotic stability of solutions of a delayed porous thermoelastic system of type III, where the delay acts on the heat equation. We investigate the cases of equal and non-equal wave speeds. In the first case, we establish an exponential rate of decay provided that the weight of the delay is strictly less than the weight of the thermal dissipation. In the case of non-equal wave speeds, we obtain a polynomial decay rate.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2023)
Article
Mathematics, Applied
Djamel Ouchenane, Abdelbaki Choucha, Mohamed Abdalla, Salah Mahmoud Boulaaras, Bahri Belkacem Cherif
Summary: The paper discusses the stability of a one-dimensional porous-elastic system with thermoelasticity of type III and distributed delay term, analyzing both cases of equal and nonequal speeds of wave propagation. It establishes the well-posedness of the system and uses energy methods combined with Lyapunov functions for the analysis.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Mathematics, Applied
Fouzia Foughali, Salah Zitouni, Lamine Bouzettouta, Houssem Eddine Khochemane
Summary: In this paper, we study the well-posedness of a porous-elastic system with microtemperatures and a time-varying delay term in the internal feedback. We prove exponential stabilization of the system when the wave speeds are equal by introducing a suitable Lyapunov functional. Furthermore, we show that the system exhibits polynomial stability when the wave speeds are not equal.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Materials Science, Multidisciplinary
Lorenzo Liverani, Ramon Quintanilla
Summary: In this paper, a model of poro-thermoelasticity with microtemperatures is investigated. The well-posedness of the resulting system and the exponential decay of energy are proven.
MATHEMATICS AND MECHANICS OF SOLIDS
(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)
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, Applied
A. J. A. Ramos, C. A. S. Nonato, A. D. S. Campelo, M. M. Freitas, D. W. G. Silva
Summary: In this work, the piezoelectric beams model with second sound is considered, where the thermal effect is given by the Cattaneo's law of heat conduction. The existence and uniqueness of solutions of the system are proved using semigroup theory, and the exponential stability of the system is proven using the energy method with multiplier techniques.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(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)
