TY - JOUR
T1 - Global existence for a nonlinear system in thermoviscoelasticity with nonconvex energy
AU - Zimmer, Johannes
N1 - Funding Information:
This paper developed from a part of the author’s Ph.D. thesis [27] written under the supervision of Prof. Jürgen Scheurle and Prof. Karl-Heinz Hoffmann. I thank both of them for support and advice. The article was written while the author held a postdoctoral position in the Division of Engineering and Applied Science, California Institute of Technology. This research has been supported by the Deutsche Forschungsgemeinschaft, SFB 438, and an NSF-ITR grant (ACI-0204932). Helpful comments from the referees are gratefully acknowledged.
PY - 2004/4/15
Y1 - 2004/4/15
N2 - A three-dimensional thermoviscoelastic 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 L1 data.
AB - A three-dimensional thermoviscoelastic 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 L1 data.
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
AN - SCOPUS:1942508042
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 -