On the thermoelasticity with several dissipative mechanisms of type III

Quintanilla²

2023

Eur. J. Appl. Math

Self Cite

In this paper, we consider the time decay of the solutions to some problems arising in strain gradient thermoelasticity. We restrict to the two-dimensional case, and we assume that two dissipative mechanisms are introduced, the temperature and the mass dissipation. First, we show that this problem is well-posed proving that the operator defining it generates a contractive semigroup of linear operators. Then, assuming that the function involving the coupling terms is elliptic, the exponential decay of the solutions is concluded as well as the analyticity of the solutions. Finally, we describe how to obtain the exponential stability in the case of hyperbolic dissipation.

Section: Introductionmentioning

confidence: 99%

-coupling mechanisms are sufficient to obtain exponential decay in strain gradient elasticity

Quintanilla²

2023

Eur. J. Appl. Math

Self Cite

On the hyperbolic thermoelasticity with several dissipation mechanisms

Quintanilla

2023

Arch Appl Mech

In this work, we study a two-dimensional problem involving a thermoelastic body with four dissipative mechanisms. The well-known theory proposed by Lord and Shulman is used. The existence and uniqueness of solution is proved by using theory of linear semigroups. Then, introducing some assumptions of the coupling coefficients, we prove that the energy decay is exponential. An extension to the theory provided by Green and Lindsay is briefly presented and to the three-dimensional case is also commented.

Numerical analysis of a problem of elasticity with several dissipation mechanisms

Bazarra

Quintanilla³

2022

Meccanica

In this work, we numerically study a problem including several dissipative mechanisms. A particular case involving the symmetry of the coupling matrix and three mechanisms is considered, leading to the exponential decay of the corresponding solutions. Then, a fully discrete approximation of the general case in two dimensions is introduced by using the finite element method and the implicit Euler scheme. A priori error estimates are obtained and the linear convergence is derived under some appropriate regularity conditions on the continuous solution. Finally, some numerical simulations are performed to illustrate the numerical convergence and the behavior of the discrete energy depending on the number of dissipative mechanisms.