Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type

Details Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type

2011-04-13

arxiv.org/abs/1104.2395v1

Mathematics

Analysis of PDEs

22

Scientific paper

This paper is devoted to study a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under suitable conditions, we prove that any weak solutions with negative initial energy will blow up in finite time. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results

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