Math. Model. Nat. Phenom.
Volume 17, 2022
Recent Trends in Hyperbolic Equations in Physical Systems
|Number of page(s)||24|
|Published online||20 October 2022|
Mathematical modelling in nonlocal Mindlin’s strain gradient thermoelasticity with voids
Université de Carthage, Ecole Nationale d’Ingénieurs de Bizerte, 7035, BP66, Tunisia
2 UR Systémes dynamiques et applications, UR 17ES21, Bizerte, Tunisia
* Corresponding author: email@example.com
Accepted: 9 September 2022
A nonlocal theory for thermoelastic materials with voids based on Mindlin’s strain gradient theory was derived in this paper with some qualitative properties. We have also established the size effect of nonlocal heat conduction with the aids of extended irreversible thermodynamics and generalized free energy. The obtained system of equations is a coupling of three equations with higher gradients terms due to the length scale parameters ϖ and l. This poses some new mathematical difficulties due to the lack of regularity. Based on nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions to the one dimensional problem. By an approach based on the Gearhart-Herbst-Prüss-Huang theorem, we prove that the associated semigroup is exponentially stable; but not analytic.
Mathematics Subject Classification: 35L75 / 74F05 / 74H40 / 35Q74
Key words: Nonlocality / Mindlin’s strain gradientnt / Porous elasticity / nonlocal heat conduction / Exponential stability / Lack of analyticity
© The authors. Published by EDP Sciences, 2022
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