TY - JOUR
T1 - Global Solvability in Thermoelasticity with Second Sound on the Semi-axis
AU - Hu , Yuxi
JO - Journal of Partial Differential Equations
VL - 2
SP - 139
EP - 170
PY - 2012
DA - 2012/06
SN - 25
DO - http://doi.org/10.4208/jpde.v25.n2.3
UR - https://global-sci.org/intro/article_detail/jpde/5180.html
KW - Second sound
KW - linear decay rates
KW - semi-axis
KW - global solution
AB - <p>In this paper, we consider initial boundary value problem for the equations of one-dimensional nonlinear thermoelasticity with second sound in R^+. First, we derive decay rates for linear systems which, in fact, is a hyperbolic systems with a damping term. Then, using this linear decay rates, we get L^1 and L^∞ decay rates for nonlinear systems. Finally, combining with L^2 estimates and a local existence theorem, we prove a global existence and uniqueness theorem for small smooth data.</p>