Blow up of Solutions for a Nonlinear Petrovsky Type Equation with Time-dependent Coefficients

• 作者: Xiao-xiao ZHENG Ya-dong SHANG Xiao-ming PENG
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 836-846
• 页数: 11页
• 语种: 英文

摘要

In this paper,we study a nonlinear Petrovsky type equation with nonlinear weak damping,a superlinear source and time-dependent coefficients utt+Δ2u+k1(t)|ut|m-2ut=k2(t)|u|p-2u,x ∈ Ω,t＞0,where Ω is a bounded domain in Rn.Under certain conditions on k1(t),k2(t)and the initial-boundary data,the upper bound for blow-up time of the solution with negative initial energy function is given by means of an auxiliary functional and an energy estimate method if p＞m.Also,a lower bound of blow-up time are obtained by using a Sobolev-type inequality and a first order differential inequality technique for n=2,3 and n＞4.