Existence and Blow up Time Estimate for a Negative Initial Energy Solution of a Nonlinear Cauchy Problem

被引：7

作者：

Ogbiyele, P. A. ^{[1
]}

Arawomo, P. O. ^{[1
]}

机构：

[1] Univ Ibadan, Dept Math, Ibadan 200284, Nigeria

来源：

ACTA APPLICANDAE MATHEMATICAE | 2020年 / 170卷 / 01期

关键词：

Nonlinear wave equation; Global existence; Blow up; Finite speed of propagation; WAVE-EQUATIONS; GLOBAL NONEXISTENCE; ASYMPTOTIC-BEHAVIOR; EVOLUTION-EQUATIONS;

D O I：

10.1007/s10440-020-00341-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider nonlinear wave equations with dissipation having the form u(tt)-div(vertical bar del u vertical bar(gamma-2) del u) + b(t,x)vertical bar u(t)vertical bar(m-2) u(t) = g(x,u) for (t,x) is an element of[0, infinity) x R-n. We obtain existence and blow up results under suitable assumptions on the positive functionb (t,x)and the nonlinear functiong (x,u). The existence result was obtained using the Galerkin approach while the blow up result was obtained via the perturbed energy method. Our result improves on the perturbed energy technique for unbounded domains.

引用

页码：443 / 458

页数：16

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