Global existence and blow up of solutions for the Cauchy problem of some nonlinear wave equations

被引：0

作者：

Wei, Xiao ^{[1
]}

机构：

[1] Changan Univ, Sch Sci, Xian, Peoples R China

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2022年 / 12卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Global solutions; Blow up; Generalized Sobolev Spaces; EVOLUTION-EQUATIONS; NONEXISTENCE; INSTABILITY; DECAY; SETS;

D O I：

10.1007/s13324-021-00625-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the global existence and blow up for the Cauchy problem for some hyperbolic system u(ktt )+ delta u(kt) - phi Delta u(k) + f(k) (u(1), u(2)) = lambda vertical bar u(k)vertical bar(beta-1) u(k). k = 1, 2. Under certain conditions we prove the global existence of solutions by adapting the method of modified potential well in a functional setting of generalized Sobolev spaces, and we prove that the solution decays exponentially by introducing an appropriate Lyapunov function. By the concave method, we discuss the blow-up behavior of weak solution with certain conditions and give some estimates for the lifespan of solutions.

引用

页数：23