TY - JOUR
T1 - Large time behavior of solutions to a semilinear hyperbolic system with relatxaion
AU - Ueda, Yoshihiro
AU - Kawashima, Shuichi
PY - 2007/3
Y1 - 2007/3
N2 - We are concerned with the initial value problem for a damped wave equation with a nonlinear convection term which is derived from a semilinear hyperbolic system with relaxation. We show the global existence and asymptotic decay of solutions in W1,p (1 ≤ p ≤ ∞) under smallness condition on the initial data. Moreover, we show that the solution approaches in W1,p (1 ≤ p ≤ ∞) the nonlinear diffusion wave expressed in terms of the self-similar solution of the Burgers equation as time tends to infinity. Our results are based on the detailed pointwise estimates for the fundamental solutions to the linearlized equation.
AB - We are concerned with the initial value problem for a damped wave equation with a nonlinear convection term which is derived from a semilinear hyperbolic system with relaxation. We show the global existence and asymptotic decay of solutions in W1,p (1 ≤ p ≤ ∞) under smallness condition on the initial data. Moreover, we show that the solution approaches in W1,p (1 ≤ p ≤ ∞) the nonlinear diffusion wave expressed in terms of the self-similar solution of the Burgers equation as time tends to infinity. Our results are based on the detailed pointwise estimates for the fundamental solutions to the linearlized equation.
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U2 - 10.1142/s0219891607001082
DO - 10.1142/s0219891607001082
M3 - Article
AN - SCOPUS:34447262298
SN - 0219-8916
VL - 4
SP - 147
EP - 179
JO - Journal of Hyperbolic Differential Equations
JF - Journal of Hyperbolic Differential Equations
IS - 1
ER -