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Applicable Analysis
An International Journal
Volume 87, 2008 - Issue 4
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Original Articles

Energy decay for Porous-thermo-elasticity systems of memory type

A. Soufyane Faculty of Engineering and Applied Sciences, ALHOSN University, Abu Dhabi, UAECorrespondence[email protected]
Pages 451-464 | Received 16 Dec 2007, Accepted 05 Mar 2008, Published online: 18 Apr 2008

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B. Feng, M. M. Freitas, D. S. Almeida Júnior & A. J. A. Ramos. (2022) Quasi-stability and attractors for a porous-elastic system with history memory. Applicable Analysis 101:17, pages 6237-6254.
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Tijani A. Apalara & Abdelaziz Soufyane. (2022) Energy decay for a weakly nonlinear damped porous system with a nonlinear delay. Applicable Analysis 101:17, pages 6113-6135.
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M. L. Santos, S. M. S. Cordeiro & E. S. Maciel. (2022) On the porous thermoelastic system with Coleman–Gurtin law. Applicable Analysis 101:13, pages 4432-4452.
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M. L. Santos, A. D. S. Campelo & M. L. S. Oliveira. (2019) On porous-elastic systems with Fourier law. Applicable Analysis 98:6, pages 1181-1197.
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Mounir Afilal & Abdelaziz Soufyane. (2019) General decay for a porous thermoelastic system with a memory. Applicable Analysis 98:3, pages 638-650.
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Tijani A. Apalara. (2019) On the stability of porous-elastic system with microtemparatures. Journal of Thermal Stresses 42:2, pages 265-278.
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Baowei Feng. (2018) Uniform decay of energy for a porous thermoelasticity system with past history. Applicable Analysis 97:2, pages 210-229.
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Belkacem Said-Houari & Salim A. Messaoudi. (2013) Decay property of regularity-loss type of solutions in elastic solids with voids. Applicable Analysis 92:12, pages 2487-2507.
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Moncef Aouadi & Abdelaziz Soufyane. (2010) Polynomial and exponential stability for one-dimensional problem in thermoelastic diffusion theory. Applicable Analysis 89:6, pages 935-948.
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Muhammad I. Mustafa, Adel M. Al-Mahdi & Mohammad M. Al-Gharabli. (2023) Theoretical Decay Results of a Swelling Soils System with Frictional Damping Versus Viscoelastic Damping. Mediterranean Journal of Mathematics 20:5.
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Mohammad M. Kafini, Mohammed M. Al-Gharabli & Adel M. Al-Mahdi. (2023) Asymptotic Behavior of Solutions to a Nonlinear Swelling Soil System with Time Delay and Variable Exponents. Mathematical and Computational Applications 28:5, pages 94.
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Haiyan Li & Baowei Feng. (2023) Exponential and Polynomial Decay Rates of a Porous Elastic System with Thermal Damping. Journal of Function Spaces 2023, pages 1-11.
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Baowei Feng & Ahmet Özkan Özer. (2023) Stability results for piezoelectric beams with long‐range memory effects in the boundary. Mathematische Nachrichten.
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A. M. Al-Mahdi, M. M. Al-Gharabli, I. Kissami, A. Soufyane & M. Zahri. (2023) Exponential and polynomial decay results for a swelling porous elastic system with a single nonlinear variable exponent damping: theory and numerics. Zeitschrift für angewandte Mathematik und Physik 74:2.
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Le Thi Phuong Ngoc, Pham Nguyen Nhat Khanh, Nguyen Huu Nhan & Nguyen Thanh Long. (2022) On a nonlinear boundary problem for thermoelastic coupled beam equations with memory term. Mathematical Methods in the Applied Sciences 46:4, pages 3614-3648.
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Yuming Qin, Jaime E. Muñoz Rivera & To Fu Ma. (2022) Smooth dynamics of a Timoshenko system with hybrid dissipation. Asymptotic Analysis 131:1, pages 109-123.
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B.M.R. Calsavara, E.H. Gomes Tavares & M.A. Jorge Silva. (2022) Exponential stability for a thermo-viscoelastic Timoshenko system with fading memory. Journal of Mathematical Analysis and Applications 512:2, pages 126147.
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Quang-Minh Tran, Thi-Thi Vu & Mirelson M. Freitas. (2022) Blow-up of weak solutions for a porous elastic system with nonlinear damping and source terms. Journal of Mathematical Analysis and Applications 512:1, pages 126132.
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Adel M. Al-Mahdi, Mohammad Kafini, Jamilu Hashim Hassan & Mohamed Alahyane. (2022) Well-posedness, theoretical and numerical stability results of a memory-type porous thermoelastic system. Zeitschrift für angewandte Mathematik und Physik 73:3.
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Tijani A. Apalara & Aminat O. Ige. (2022) Exponential Stability for the Equations of Porous Elasticity in One-Dimensional Bounded Domains. Mathematics 10:9, pages 1597.
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Adel M. Al-Mahdi, Mohammad M. Al-Gharabli & Mohamed Alahyane. (2022) Theoretical and Computational Results of a Memory-Type Swelling Porous-Elastic System. Mathematical and Computational Applications 27:2, pages 27.
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ABDELBAKI CHOUCHA, SALAH BOULAARAS, DJAMEL OUCHENANE, ASMA ALHARBI & MOHAMED ABDALLA. (2021) GLOBAL EXISTENCE OF TIMOSHENKO SYSTEM WITH RESPECT TO FRACTIONAL MEMORY OPERATOR, SPATIAL FRACTIONAL THERMAL EFFECT AND DISTRIBUTED DELAY. Fractals 30:01.
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M. L. Santos, D. S. Almeida Júnior & S. M. S. Cordeiro. (2021) Energy decay for a porous-elastic system with nonlinear localized damping. Zeitschrift für angewandte Mathematik und Physik 73:1.
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Marcio A. Jorge Silva & Sandro B. Pinheiro. (2022) A new perspective of exponential stability for Timoshenko systems under history and thermal effects1. Asymptotic Analysis 127:3, pages 217-248.
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Hugo D. Fernández Sare & Ramón Quintanilla. (2021) Porous-elastic Plates: Fourier Versus Type III. Applied Mathematics & Optimization 84:S1, pages 1055-1085.
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Djellali Fayssal. (2021) General decay for memory-type porous elastic system with thermoelasticity of type III. Ricerche di Matematica.
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Adel M. Al-Mahdi, Mohammad M. Al-Gharabli & Salim A. Messaoudi. (2021) New general decay of solutions in a porous-thermoelastic system with infinite memory. Journal of Mathematical Analysis and Applications 500:1, pages 125136.
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A. Magaña & R. Quintanilla. (2021) Decay of quasi-static porous-thermo-elastic waves. Zeitschrift für angewandte Mathematik und Physik 72:3.
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Baowei Feng, Ling Yan & Dilberto da Silva Almeida Júnior. (2020) Stabilization for an inhomogeneous porous‐elastic system with temperature and microtemperature. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 101:6.
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Abdelhak Djebabla, Abdelbaki Choucha, Djamel Ouchenane & Khaled Zennir. (2021) Explicit Stability for a Porous Thermoelastic System with Second Sound and Distributed Delay Term. International Journal of Applied and Computational Mathematics 7:2.
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M.A. Jorge Silva & R. Racke. (2021) Effects of history and heat models on the stability of thermoelastic Timoshenko systems. Journal of Differential Equations 275, pages 167-203.
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Adel M. Al-Mahdi, Mohammad M. Al-Gharabli & Mohamed Alahyane. (2021) Theoretical and numerical stability results for a viscoelastic swelling porous-elastic system with past history. AIMS Mathematics 6:11, pages 11921-11949.
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Hanni Dridi & Abdelhak Djebabla. (2019) On the stabilization of linear porous elastic materials by microtemperature effect and porous damping. ANNALI DELL'UNIVERSITA' DI FERRARA 66:1, pages 13-25.
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Tijani A. Apalara. (2019) On the Stabilization of a Memory-Type Porous Thermoelastic System. Bulletin of the Malaysian Mathematical Sciences Society 43:2, pages 1433-1448.
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Ahmed Keddi. (2020) Exponential Decay for a Porous Thermoelastic System with Second Sound. Exponential Decay for a Porous Thermoelastic System with Second Sound.
Wenjun Liu, Dongqin Chen & Salim A. Messaoudi. (2020) General decay rates for one-dimensional porous-elastic system with memory: The case of non-equal wave speeds. Journal of Mathematical Analysis and Applications 482:2, pages 123552.
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Baowei Feng & Mingyang Yin. (2018) Decay of solutions for a one-dimensional porous elasticity system with memory: the case of non-equal wave speeds. Mathematics and Mechanics of Solids 24:8, pages 2361-2373.
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Tijani A. Apalara. (2018) A General Decay for a Weakly Nonlinearly Damped Porous System. Journal of Dynamical and Control Systems 25:3, pages 311-322.
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Mohammad M. Al-Gharabli & Salim A. Messaoudi. (2019) Well-posedness and a general decay for a nonlinear damped porous thermoelastic system with second sound. Georgian Mathematical Journal 26:1, pages 1-11.
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Baowei Feng & Tijani A. Apalara. (2019) Optimal decay for a porous elasticity system with memory. Journal of Mathematical Analysis and Applications 470:2, pages 1108-1128.
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Tijani A. Apalara. (2019) General decay of solutions in one-dimensional porous-elastic system with memory. Journal of Mathematical Analysis and Applications 469:2, pages 457-471.
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Mohammad M. Al-Gharabli. (2017) On the long-time behavior of a nonlinear damped porous thermoelastic system with second sound. Afrika Matematika 29:1-2, pages 211-221.
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M. L. Santos, A. D. S. Campelo & D. S. Almeida Júnior. (2017) Rates of Decay for Porous Elastic System Weakly Dissipative. Acta Applicandae Mathematicae 151:1, pages 1-26.
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Wenjun Liu & Miaomiao Chen. (2017) Well-posedness and exponential decay for a porous thermoelastic system with second sound and a time-varying delay term in the internal feedback. Continuum Mechanics and Thermodynamics 29:3, pages 731-746.
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Mounir Afilal, Salim Messaoudi & Abdelaziz Soufyane. (2017) Stabilization of a coupled hyperbolic equations with a heat equation of second sound. Mediterranean Journal of Mathematics 14:2.
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M.L. Santos & D.S. Almeida Júnior. (2017) On the porous-elastic system with Kelvin–Voigt damping. Journal of Mathematical Analysis and Applications 445:1, pages 498-512.
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Abdelfeteh Fareh & Salim A. Messaoudi. (2017) Energy decay for a porous thermoelastic system with thermoelasticity of second sound and with a non-necessary positive definite energy. Applied Mathematics and Computation 293, pages 493-507.
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Jianghao Hao & Peipei Wang. (2016) Asymptotical stability for memory‐type porous thermoelastic system of type III with constant time delay. Mathematical Methods in the Applied Sciences 39:13, pages 3855-3865.
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Zhuangyi Liu, Antonio Maga?a & Ram?n Quintanilla. (2016) On the time decay of solutions for non-simple elasticity with voids. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f?r Angewandte Mathematik und Mechanik 96:7, pages 857-873.
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M. L. Santos & D. S. Almeida Júnior. (2016) On porous-elastic system with localized damping. Zeitschrift für angewandte Mathematik und Physik 67:3.
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Antonio Magaña & Ramón Quintanilla. (2015) Exponential decay in nonsimple thermoelasticity of type III. Mathematical Methods in the Applied Sciences 39:2, pages 225-235.
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M. Carme Leseduarte, Antonio Magaña & Ramón Quintanilla. (2015) On the time decay of solutions in micropolar viscoelasticity. Meccanica 50:7, pages 1761-1774.
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Salim A. Messaoudi & Abdelfeteh Fareh. (2015) Exponential decay for linear damped porous thermoelastic systems with second sound. Discrete and Continuous Dynamical Systems - Series B 20:2, pages 599-612.
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Salim A. Messaoudi & Tijani A. Apalara. (2014) General stability result in a memory-type porous thermoelasticity system of type III. Arab Journal of Mathematical Sciences 20:2, pages 213-232.
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Antonio Magaña & Ramón Quintanilla. (2014) On the uniqueness and analyticity of solutions in micropolar thermoviscoelasticity. Journal of Mathematical Analysis and Applications 412:1, pages 109-120.
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Leila Djouamai & Belkacem Said-Houari. (2014) Decay property of regularity-loss type for solutions in elastic solids with voids. Journal of Mathematical Analysis and Applications 409:2, pages 705-715.
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Jaime E Muñoz Rivera, Paulo Xavier Pamplona & Ramón Quintanilla. (2012) On decay and analyticity in viscoelastic solids with voids by means of dissipative coupling. Mathematics and Mechanics of Solids 18:8, pages 837-848.
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Salim A. MESSAOUDI & Abdelfeteh FAREH. (2013) General decay for a porous-thermoelastic system with memory: The case of nonequal speeds. Acta Mathematica Scientia 33:1, pages 23-40.
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Paulo Xavier Pamplona, Jaime E. Muñoz Rivera & Ramón Quintanilla. (2012) Analyticity in porous-thermoelasticity with microtemperatures. Journal of Mathematical Analysis and Applications 394:2, pages 645-655.
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Moncef Aouadi, Barbara Lazzari & Roberta Nibbi. (2012) Exponential decay in thermoelastic materials with voids and dissipative boundary without thermal dissipation. Zeitschrift für angewandte Mathematik und Physik 63:5, pages 961-973.
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Zhong-Jie Han & Gen-Qi Xu. (2012) Exponential decay in non-uniform porous-thermo-elasticity model of Lord-Shulman type. Discrete & Continuous Dynamical Systems - B 17:1, pages 57-77.
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Salim A. Messaoudi & Abdelfeteh Fareh. (2011) General decay for a porous thermoelastic system with memory: The case of equal speeds. Nonlinear Analysis: Theory, Methods & Applications 74:18, pages 6895-6906.
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Hugo D. Fernández Sare, Jaime E. Muñoz Rivera & Ramón Quintanilla. (2011) On the rate of decay in interacting continua with memory. Journal of Differential Equations 251:12, pages 3583-3605.
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Paulo Xavier Pamplona, Jaime E. Muñoz Rivera & Ramón Quintanilla. (2011) On the decay of solutions for porous-elastic systems with history. Journal of Mathematical Analysis and Applications 379:2, pages 682-705.
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Moncef Aouadi. (2011) Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound. International Journal of Differential Equations 2011, pages 1-21.
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A. Soufyane, M. Afilal, T. Aouam & M. Chacha. (2010) General decay of solutions of a linear one-dimensional porous-thermoelasticity system with a boundary control of memory type. Nonlinear Analysis: Theory, Methods & Applications 72:11, pages 3903-3910.
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Barbara Lazzari & Roberta Nibbi. (2009) On the influence of a dissipative boundary on the energy decay for a porous elastic solid. Mechanics Research Communications 36:5, pages 581-586.
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Abdelaziz Soufyane, Mounir Afilal & Mama Chacha. (2009) Boundary Stabilization of Memory Type for the Porous-Thermo-Elasticity System. Abstract and Applied Analysis 2009, pages 1-17.
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