Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity

DOI10.1007/BF00251248zbMath0481.73009MaRDI QIDQ1162378

Marshall Slemrod

Publication date: 1981

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

zbMATH Keywords

nonlinear evolution equationsFaedo-Galerkin methodcontraction mappingfinite thermoelastic deformationsfree energy density depends 'genuinely' on deformation gradient and temperatureglobal existence- uniquenesslocal existence- uniquenessrefined version of energy method

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elasticity (74B20) Thermal effects in solid mechanics (74F05) Bifurcations in context of PDEs (35B32) Uniqueness of solutions of dynamical problems in solid mechanics (74H25) Uniqueness of solutions of equilibrium problems in solid mechanics (74G30)

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Cites Work

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• Energy methods for nonlinear hyperbolic volterra integrodifferential equations
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• Global existence for nonlinear wave equations
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• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
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