TY - JOUR
T1 - Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy
AU - Zimmer, J
N1 - ID number: ISI:000221110800021
PY - 2004/4/15
Y1 - 2004/4/15
N2 - A three-dimensional thermoviscoclastic system derived from the balance laws of momentum and energy is considered. To describe structural phase transitions in solids, the stored energy function is not assumed to be convex as a function of the deformation gradient. A novel feature for multidimensional, nonconvex, and nonisothermal problems is that no regularizing higher-order terms are introduced. The mechanical dissipation is not linearized. We prove existence global in time. The approach is based on a fixed-point argument using an implicit time discretization and the theory of renormalized solutions for parabolic equations with L-1 data. (C) 2004 Elsevier Inc. All rights reserved.
AB - A three-dimensional thermoviscoclastic system derived from the balance laws of momentum and energy is considered. To describe structural phase transitions in solids, the stored energy function is not assumed to be convex as a function of the deformation gradient. A novel feature for multidimensional, nonconvex, and nonisothermal problems is that no regularizing higher-order terms are introduced. The mechanical dissipation is not linearized. We prove existence global in time. The approach is based on a fixed-point argument using an implicit time discretization and the theory of renormalized solutions for parabolic equations with L-1 data. (C) 2004 Elsevier Inc. All rights reserved.
UR - http://dx.doi.org/10.1016/j.jmaa.2003.12.010
UR - https://www.scopus.com/pages/publications/1942508042
U2 - 10.1016/j.jmaa.2003.12.010
DO - 10.1016/j.jmaa.2003.12.010
M3 - Article
SN - 0022-247X
VL - 292
SP - 589
EP - 604
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -