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The Faedo-Galerkin method in thermal stresses theory. (English) Zbl 0645.73009

The author formulates five boundary initial value problems for classical and generalized linear thermoelasticity, taking into account inhomogeneous, anisotropic material behaviour. He proves the existence and uniqueness of weak solutions for the above mentioned problems using the Faedo-Galerkin method. Further the continuous dependence of the solutions on given data is demonstrated. In the last section the regularity of the weak solutions with respect to the space and time variables is studied. The proofs are based on methods of functional analysis.
Reviewer: H.Bufler

MSC:

74F05 Thermal effects in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35A15 Variational methods applied to PDEs
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