Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity

DOI10.1007/BF00375601zbMath0756.73012MaRDI QIDQ1181006

Reinhard Racke, Yoshihiro Shibata

Publication date: 27 June 1992

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

homogeneous boundary conditionsglobal existence theoremdisplacement-temperature initial-boundary value problem

Mathematics Subject Classification ID

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Cites Work

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• On the global existence of classical solutions of second order fully nonlinear hyperbolic equations with first order dissipation in the exterior domain
• On formation of singularities in one-dimensional nonlinear thermoelasticity
• On the Cauchy problem in nonlinear 3-D-thermoelasticity
• Smooth global solutions for the one-dimensional equations in magnetohydrodynamics
• On a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain
• Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity
• Global existence of small solutions to the initial value problem for nonlinear thermoelasticity
• Mixed problems for hyperbolic equations of second order
• On smooth solutions of the Cauchy problem in one-dimensional nonlinear thermoelasticity
• Global existence of smooth solutions in one-dimensional nonlinear thermoelasticity
• Blow-up in non-linear three-dimensional thermoelasticity
• On some quasilinear hyperbolic-parabolic initial boundary value problems
• Development of singularities in solutions of the equations of nonlinear thermoelasticity

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