2026-04-05T10:45:36Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/3626542026-01-30T08:59:20Zcom_2072_1033col_2072_452950

On the time decay for the MGT-type porosity problems Baldonedo, Jacobo Fernández, Jose R. Quintanilla de Latorre, Ramón Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències Finite element method Porosity MGT-porosity Dissipation mechanisms Existence and uniqueness Energy decay Finite elements Numerical behaviour Elements finits, Mètode dels Porositat Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions Classificació AMS::65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems In this work we study three different dissipation mechanisms arising in the so-called Moore-Gibson-Thompson porosity. The three cases correspond to the MGT-porous hyperviscosity (fourth-order term), the MGT-porous viscosity (second-order term) and the MGT-porous weak viscosity (zerothorder term). For all the cases, we prove that there exists a unique solution to the problem and we analyze the resulting point spectrum. We also show that there is an exponential energy decay for the first case, meanwhile for the second and third case only a polynomial decay is found. Finally, we present some one-dimensional numerical simulations to illustrate the behaviour of the discrete energy for each case This paper is part of the projects PGC2018-096696-B-I00 and PID2019-105118GB-I00, funded by the Spanish Ministry of Science, Innovation and Universities and FEDER "A way to make Europe". Peer Reviewed Postprint (author's final draft) 2022-08 Article info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105118GB-I00/ES/ANALISIS MATEMATICO APLICADO A LA TERMOMECANICA/ Open Access American Institute of Mathematical Sciences