摘要
本文研究任意维数的强阻尼非线性波动方程u_(tt)—α△u_t-△u=f(u)具第一类齐边界条件的初边值问题,设f∈C^1,f＇(u)上方有界,且当n≥4时存在常数A,B和户,使|f＇(u)|≤A|u|~p+B,其中0<p≤4/(n—4)(n>4);0<p<∞(n=4),得到唯一整体强解,从而改进和推广了已知结果。
In this paper we study the initial-boundary value problem with first homogeneous boundary condition for the strongly damped nonlinear wave equation in arbitrary dimensions. Suppose that is upper bounded and when n>4, there exist
A,B and p such that then the unique global strong solution can be obtained, so the known results are improved and generalized.
出处
《应用数学》
CSCD
北大核心
1995年第3期262-266,共5页
Mathematica Applicata
关键词
强阻尼
非线性
波动方程
初边值问题
Strongly damp
Nonlinear wave equation
Arbitrary dimensions
Initial-boundary value
