$$n^2$$ of dissipative couplings are sufficient to guarantee the exponential decay in elasticity

descriptionPublicationkeyboard_double_arrow_right Article 06 Jul 2022 English Publisher:Springer Science and Business Media LLCJournal:Ricerche di Matematica, volume 73, pages 2,243-2,253 (issn: 0035-5038, eissn: 1827-3491,

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Authors: Fernández García, José Ramon; Quintanilla de Latorre, Ramón;

doi: 10.1007/s11587-022-00719-z

handle: 2117/374631

$$n^2$$ of dissipative couplings are sufficient to guarantee the exponential decay in elasticity

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Abstract

AbstractIn this paper, we prove that the solutions to the problem determined by an elastic material with $$n^2$$ n 2 coupling dissipative mechanisms decay in an exponential way for every (bounded) geometry of the body, where n is the dimension of the domain, and whenever the coupling coefficients satisfy a suitable condition. We also give several examples where the solutions do not decay when the rank of the matrix of the coupling mechanisms is less than $$n^2$$ n 2 (2 in dimension 2 and 6 in dimension 3).

Related Organizations

Universitat Polit?cnica de Catalunya
Spain
Universitat Politècnica de Catalunya
Spain
Universitat Polite`cnica de Catalunya
Spain
Universidade de Vigo
Spain

Keywords

Classificació AMS::35 Partial differential equations::35L Partial differential equations of hyperbolic type, coupling coefficient matrix, Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects, Classificació AMS::74 Mechanics of deformable solids::74H Dynamical problems, existence, uniqueness, Energy decay, Long-time behavior of solutions for dynamical problems in solid mechanics, dissipation mechanism, 510, Dissipation mechanism, Thermal effects in solid mechanics, thermoelasticity, Existence of solutions of dynamical problems in solid mechanics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències, Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions, PDEs in connection with mechanics of deformable solids, energy decay, undamped solution, Thermoelasticity, Termoelasticitat

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