Global Existence and Asymptotic Behavior in Nonlinear Thermoviscoelasticity
نویسنده
چکیده
We study global existence, uniqueness, and asymptotic behavior, as time tends to infinity, of weak solutions to the system of nonlinear thermoviscoelasticity. Various boundary conditions are considered. It is shown that for any initial data (u0 , v0 , %0) # L _W 1, _H 1 there is a unique global solution (u, v, %)=(deformation gradient, velocity, temperature) such that u # C([0, ], L ), v # C((0, ), W 1, ) & L ([0, ), W 1, ), % # C([0, ), H). The constitutive assumptions for the Helmholtz free energy include the models for the study of phase transition problems in shape memory alloys. 1997 Academic Press
منابع مشابه
Global Existence of the Higher-Dimensional Linear System of Thermoviscoelasticity
Zhiyong Ma College of Science, Shanghai Second Polytechnic University, Shanghai 201209, China Correspondence should be addressed to Zhiyong Ma, [email protected] Received 4 May 2011; Revised 28 June 2011; Accepted 30 June 2011 Academic Editor: Stanisław Migórski Copyright q 2011 Zhiyong Ma. This is an open access article distributed under the Creative Commons Attribution License, which ...
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