Existence and asymptotic stability for generalized elasticity equation with variable exponent

• Autorzy: Dilmi Mohamed , Otmani Sadok

Identyfikatory

DOI

10.7494/OpMath.2023.43.3.409

• Języki publikacji: EN

Abstrakty

EN

In this paper we propose a new mathematical model describing the deformations of an isotropic nonlinear elastic body with variable exponent in dynamic regime. We assume that the stress tensor σp(·) has the form σp(·)(u) =(2μ + |d(u)|p(·)−2) d(u) + λTr (d(u)) I3, where u is the displacement field, μ, λ are the given coefficients d(·) and I3 are the deformation tensor and the unit tensor, respectively. By using the Faedo-Galerkin techniques and a compactness result we prove the existence of the weak solutions, then we study the asymptotic behaviour stability of the solutions.

Słowa kluczowe

EN

asymptotic stability; variable exponent Lebesgue; Sobolev spaces; generalized elasticity equation

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 3
• Strony: 409--428
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Dilmi Mohamed

• University of Blida 1, Department of Mathematics, LAMDA-RO Laboratory, PO Box 270 Route de Soumaa, Blida, Algeria

• https://orcid.org/0000-0003-2114-8891

autor

Otmani Sadok

• University of Kasdi Merbah-Ouargla, Department of Mathematics, Ouargla, Algeria

• https://orcid.org/0000-0001-8625-6602

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)