Dual-phase-lag one-dimensional thermo-porous-elasticity with microtemperatures

This paper is devoted to studying the linear system of partial differential equations modelling a one-dimensional thermo-porous-elastic problem with microtemperatures in the context of the dual-phase-lag heat conduction. Existence, uniqueness, and exponential decay of solutions are proved. Polynomial stability is also obtained in the case that the relaxation parameters satisfy a certain equality. Our arguments are based on the theory of semigroups of linear operators.

[1]  B. Feng,et al.  Decay of solutions for a one-dimensional porous elasticity system with memory: the case of non-equal wave speeds , 2019 .

[2]  P. Říha.  On the theory of heat-conducting micropolar fluids with microtemperatures , 1975 .

[3]  Stephen C. Cowin,et al.  A nonlinear theory of elastic materials with voids , 1979 .

[4]  R. Grot.  Thermodynamics of a continuum with microstructure , 1969 .

[5]  Zhuangyi Liu,et al.  Time decay in dual-phase-lag thermoelasticity: critical case , 2017 .

[6]  R. Quintanilla,et al.  On the time decay of solutions in porous-elasticity with quasi-static microvoids , 2007 .

[7]  R. Quintanilla.  A CONDITION ON THE DELAY PARAMETERS IN THE ONE-DIMENSIONAL DUAL-PHASE-LAG THERMOELASTIC THEORY , 2003 .

[8]  Zhuangyi Liu,et al.  Dual‐phase‐lag heat conduction with microtemperatures , 2021, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik.

[9]  Dorin Ieşan,et al.  A theory of thermoelastic materials with voids , 1986 .

[10]  Yuri Tomilov,et al.  Optimal polynomial decay of functions and operator semigroups , 2009, 0910.0859.

[11]  A. Eringen.  Microcontinuum Field Theories , 2020, Advanced Continuum Theories and Finite Element Analyses.

[12]  On the existence and uniqueness in phase-lag thermoelasticity , 2018 .

[13]  P. Říha,et al.  On the microcontinuum model of heat conduction in materials with inner structure , 1976 .

[14]  Alain Miranville,et al.  Exponential decay in one-dimensional type II thermoviscoelasticity with voids , 2020, J. Comput. Appl. Math..

[15]  Ramón Quintanilla,et al.  Exponential decay in one-dimensional type III thermoelasticity with voids , 2019, Appl. Math. Lett..

[16]  S. Cowin.  The viscoelastic behavior of linear elastic materials with voids , 1985 .

[17]  Upc,et al.  ON THE EXISTENCE AND UNIQUENESS IN PHASE-LAG THERMOELASTICITY , 2017 .

[18]  D. S. Almeida Júnior,et al.  On the Decay Rates of Porous Elastic Systems , 2017 .

[19]  Stephen C. Cowin,et al.  Linear elastic materials with voids , 1983 .

[20]  R. Quintanilla,et al.  Exponential stability in thermoelasticity with microtemperatures , 2005 .

[21]  D. S. Almeida Júnior,et al.  Stabilization for an inhomogeneous porous‐elastic system with temperature and microtemperature , 2020, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik.

[22]  D. Ieşan.  THERMOELASTICITY OF BODIES WITH MICROSTRUCTURE AND MICROTEMPERATURES , 2007 .

[23]  Antonio Magaña,et al.  On the exponential decay of solutions in one-dimensional generalized porous-thermo-elasticity , 2006, Asymptot. Anal..

[24]  R. Quintanilla,et al.  Exponential stability in type III thermoelasticity with microtemperatures , 2018, Zeitschrift für angewandte Mathematik und Physik.

[25]  Ciro D'Apice,et al.  On the theory of thermoelasticity with microtemperatures , 2013 .

[26]  M. C. Leseduarte,et al.  ON THE TIME DECAY OF SOLUTIONS IN POROUS-THERMO-ELASTICITY OF TYPE II , 2009 .

[27]  G. Viccione,et al.  Rayleigh waves in isotropic strongly elliptic thermoelastic materials with microtemperatures , 2017, 2103.10785.

[28]  M. I. M. Copetti,et al.  Numerical analysis of a dual-phase-lag model with microtemperatures , 2021 .

[29]  A. J. A. Ramos,et al.  A new exponential decay result for one-dimensional porous dissipation elasticity from second spectrum viewpoint , 2020, Appl. Math. Lett..

[30]  B. Feng,et al.  Optimal decay for a porous elasticity system with memory , 2019, Journal of Mathematical Analysis and Applications.

[31]  José R. Fernández,et al.  A thermoelastic problem with diffusion, microtemperatures, and microconcentrations , 2018, Acta Mechanica.

[32]  Ramón Quintanilla,et al.  Qualitative Aspects in Dual-Phase-Lag Thermoelasticity , 2006, SIAM J. Appl. Math..

[33]  Marina Bosch,et al.  Thermoelastic Models Of Continua , 2016 .

[34]  R. Quintanilla,et al.  Phase-lag heat conduction: decay rates for limit problems and well-posedness , 2014 .

[35]  Yang Wang,et al.  On the phase-lag heat equation with spatial dependent lags , 2017 .

[36]  D. Tzou.  A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales , 1995 .

[37]  Stephen C. Cowin,et al.  A continuum theory for granular materials , 1972 .

[38]  R. Quintanilla,et al.  On the decay of solutions for porous-elastic systems with history ✩ , 2011 .