Global existence of small solutions to the initial value problem for nonlinear thermoelasticity

DOI10.1016/0022-0396(90)90016-IzbMath0725.35065OpenAlexW2055955724MaRDI QIDQ2276671

Gustavo Ponce, Reinhard Racke

Publication date: 1990

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(90)90016-i

zbMATH Keywords

existenceuniquenesssmall initial datanonlinear thermoelasticityglobal smooth solutions\(L^ p\)-L\({}^ q\) estimate

Mathematics Subject Classification ID

Related Items (11)

Well posedness and numerical solution for a non-local pseudohyperbolic initial boundary value problem ⋮ Numerical solution to a nonlinear, one-dimensional problem of thermoelasticity with volume force and heat supply in a half-space ⋮ Numerical solution to a nonlinear, one-dimensional problem of anisotropic thermoelasticity with volume force and heat supply in a half-space: interaction of displacements ⋮ Global solution to the Cauchy problem for nonlinear three-dimensional thermoelasticity of nonsimple materials ⋮ Mathematical and physical aspects of the solution to the Cauchy problem for a time‐nonlocal model of thermoelasticity theory ⋮ Existence of almost everywhere solution for nonlinear hyperbolic--parabolic system ⋮ Exponential decay to a thermoelastic system with indefinite memory dissipation in a domain with moving boundary ⋮ Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity ⋮ Nonexistence results for the Cauchy problem of time fractional nonlinear systems of thermo‐elasticity ⋮ Numerical solution for a nonlinear, one-dimensional problem of thermoelasticity ⋮ THE WELL-POSEDNESS OF THE MIXED PROBLEM FOR ONE SYSTEM OF THERMOELASTICITY WITH A SINGULAR COEFFICIENT

Cites Work

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• On the Cauchy problem in nonlinear 3-D-thermoelasticity
• The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids
• Existence and non-existence of global solutions for a semilinear heat equation
• Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity
• Global existence of smooth solutions in one-dimensional nonlinear thermoelasticity
• Blow-up in non-linear three-dimensional thermoelasticity
• On “almost global” solutions to quasilinear wave equations in three space dimensions
• Global existence of small solutions to a class of nonlinear evolution equations
• Global solutions of nonlinear hyperbolic equations for small initial data
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Almost global existence of elastic waves of finite amplitude arising from small initial disturbances
• Development of singularities in solutions of the equations of nonlinear thermoelasticity
• Blow-up for quasi-linear wave equations in three space dimensions
• Finite amplitude waves in a homogeneous isotropic elastic solid
• Global existence for nonlinear wave equations

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