This paper deals with the initial boundary value problems for the semilinear wave equations with variable coefficient principal part. By virtue of compactness uniqueness argument as well as the usual energy estimates...This paper deals with the initial boundary value problems for the semilinear wave equations with variable coefficient principal part. By virtue of compactness uniqueness argument as well as the usual energy estimates, we obtain some sufficient conditions which ensure the energy admits exponent decay.展开更多
This article consider, for the following heat equation {ut/｜x｜^s-△pu=u^q,（x,t）∈Ω×（0,T）,u（x,t）=0, （x,t）∈δΩ×（0,T） ,u（x,t）=u0（x）,u0（x）≥0,u0（x） absolotely unequalto 0 the existence of ...This article consider, for the following heat equation {ut/｜x｜^s-△pu=u^q,（x,t）∈Ω×（0,T）,u（x,t）=0, （x,t）∈δΩ×（0,T） ,u（x,t）=u0（x）,u0（x）≥0,u0（x） absolotely unequalto 0 the existence of global solution under some conditions and give two sufficient conditions for the blow up of local solution in finite time, where Ω is a smooth bounded domain in R^N（N〉p）,0∈Ω,△pu=div（｜△↓｜^P-2 △↓u）,0≤s≤2,p≥2,p-1 〈q〈 ^N-p -N＋p/N-p.展开更多
文摘This paper deals with the initial boundary value problems for the semilinear wave equations with variable coefficient principal part. By virtue of compactness uniqueness argument as well as the usual energy estimates, we obtain some sufficient conditions which ensure the energy admits exponent decay.
基金The author is supported by PhD Program Scholarship Fund of ECNU 2006.
文摘This article consider, for the following heat equation {ut/｜x｜^s-△pu=u^q,（x,t）∈Ω×（0,T）,u（x,t）=0, （x,t）∈δΩ×（0,T） ,u（x,t）=u0（x）,u0（x）≥0,u0（x） absolotely unequalto 0 the existence of global solution under some conditions and give two sufficient conditions for the blow up of local solution in finite time, where Ω is a smooth bounded domain in R^N（N〉p）,0∈Ω,△pu=div（｜△↓｜^P-2 △↓u）,0≤s≤2,p≥2,p-1 〈q〈 ^N-p -N＋p/N-p.
