摘要
In this paper, we will show that under some smallness conditions, the planar diffusion wave v（x1/√＋t）is stable for a quasilinear wave equation with nonlinear damping：vtt-△f（v）＋vt＋g（vt）=0_3 x=（x1,x2…,xn）∈Rn,where v（x1/√1＋t）is the unique similar solution to the one dimensional nonlinear heat equa-tion：vt-f（v）x1 x1=0,f＇（v）〉0,v＋（∞,t）=v±,v＋≠v_.We also obtain the L∞ time decay rate whichreads‖v-v‖L∞=О（1）（1＋t）-r/4,where r=min（3,n）.To get the main result, the energy method and a newinequality have been used.
In this paper, we will show that under some smallness conditions, the planar diffusion wave v（x1/√＋t）is stable for a quasilinear wave equation with nonlinear damping：vtt-△f（v）＋vt＋g（vt）=0_3 x=（x1,x2…,xn）∈Rn,where v（x1/√1＋t）is the unique similar solution to the one dimensional nonlinear heat equa-tion：vt-f（v）x1 x1=0,f＇（v）〉0,v＋（∞,t）=v±,v＋≠v_.We also obtain the L∞ time decay rate whichreads‖v-v‖L∞=О（1）（1＋t）-r/4,where r=min（3,n）.To get the main result, the energy method and a newinequality have been used.
基金
Supported by the National Natural Science Foundation of China(No.11201301)
Shanghai University Young Teacher Training Program(No.slg12026)
