On the existence, uniqueness and stability of solutions for semi-linear generalized elasticity equation with general damping term

DOI10.1007/S10114-017-6466-YzbMath1406.35196OpenAlexW2746103950MaRDI QIDQ1686906

Abita Rahmoune

Publication date: 18 December 2017

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-017-6466-y

zbMATH Keywords

generalized Lebesgue spaceSobolev spaces with variable exponentsnonlinear internal stabilization

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Initial-boundary value problems for second-order hyperbolic equations (35L20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Second-order semilinear hyperbolic equations (35L71) Initial-boundary value problems for second-order hyperbolic systems (35L53)

Related Items (6)

General decay of a nonlinear viscoelastic wave equation with Balakrishnân-Taylor damping and a delay involving variable exponents ⋮ Multiplicity of solutions for fractional \(q(\cdot)\)-Laplacian equations ⋮ A damped elastodynamics system under the global injectivity condition: local wellposedness in \(L^p\)-spaces ⋮ Existence and asymptotic stability for generalized elasticity equation with variable exponent ⋮ Semilinear hyperbolic boundary value problem associated to the nonlinear generalized viscoelastic equations ⋮ Existence and asymptotic behavior of solutions for degenerate nonlinear Kirchhoff strings with variable-exponent nonlinearities

Cites Work

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• Lebesgue and Sobolev spaces with variable exponents
• Semilinear hyperbolic boundary value problem for linear elasticity equations
• On weak solutions for an evolution equation with exponential nonlinearities
• Calderón-Zygmund operators on generalized Lebesgue spaces Lp(⋅) and problems related to fluid dynamics
• The existence of solutions for elliptic systems with nonuniform growth
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)

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