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Asymptotic analysis for vanishing acceleration in a thermoviscoelastic system. (English) Zbl 1090.74019
Summary: We have investigated a dynamic thermoviscoelastic system [the authors, Electron. J. Differ. Equ. 2003, Paper No. 50, 15 p., electronic only (2003; Zbl 1034.74022)], establishing existence and uniqueness results for a related initial-boundary value problem. The aim of the present paper is to study the asymptotic behavior of the solution to the above problem as the acceleration forces go to zero. In particular, well-posedness and regularity results for the limit (quasistatic) problem are recovered.

MSC:
74F05 Thermal effects in solid mechanics
74D10 Nonlinear constitutive equations for materials with memory
74H20 Existence of solutions of dynamical problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
74H30 Regularity of solutions of dynamical problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
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