A quasilinear thermoviscoelastic system for shape memory alloys with temperature-dependent specific heat. (English) Zbl 1160.74017
Summary: This article extends the previous authors’ paper [SIAM J. Math. Anal. 38, No. 6, 1733–1759 (2007; Zbl 1131.35083)] on the existence of solutions to a quasilinear thermoviscoelasticity system arising in shape memory alloy theory. In the present setup we admit a modified energy equation with temperature-growing specific heat. Due to such a modification, we can solve the problem with thermomechanical nonlinearity stronger as considered in the cited work.
MSC:
74F05 | Thermal effects in solid mechanics |
76D05 | Navier-Stokes equations for incompressible viscous fluids |
74H20 | Existence of solutions of dynamical problems in solid mechanics |
74H25 | Uniqueness of solutions of dynamical problems in solid mechanics |
35Q72 | Other PDE from mechanics (MSC2000) |
80A20 | Heat and mass transfer, heat flow (MSC2010) |