Asymptotic behavior of weak solutions to nonlinear thermoviscoelastic systems with constant temperature boundary conditions

作者：Shang Chanyu^*

来源：Asymptotic Analysis, 2007, 55(3-4): 229-251.

• shape memory alloys
• asymptotic behavior
• phase transitions

This paper deals with the one-dimensional nonlinear thermoviscoelastic system subject to constant temperature boundary conditions, describing phase transitions in shape memory alloys. We shall prove the global existence and uniqueness of the weak solution for initial data (strain, velocity, absolute temperature) (u(0), v(0), theta(0)) is an element of L-infinity x W-0(1,infinity) x H-1. Furthermore, we investigate the asymptotic behavior as time tends to infinity and establish the following asymptotic properties for the weak solution: As t --> infinity, <br xmlns:set="http://exslt.org/sets">v --> 0 in H-1(0, 1),
theta --> T-0 in L-infinity(0, 1),
u(x, t) --> u(infinity)(x) a.e.,
where u(infinity) is an element of L-infinity is a stationary state satisfying
f(1)(u(infinity))T-0 + f(2)(u(infinity))=0, a.e., in [0, 1].
Here we work in a framework in which u belongs to L-infinity to describe phase transitions between different configurations of crystal lattices.

• 出版日期2007
• 单位复旦大学