Blow up of Solutions to Semilinear Wave Equations with variable coefficients and boundary

Details Blow up of Solutions to Semilinear Wave Equations with variable coefficients and boundary Blow up of Solutions to Semilinear Wave Equations with variable coefficients and boundary

2010-03-09

arxiv.org/abs/1003.1824v1

Mathematics

Analysis of PDEs

Scientific paper

This paper is devoted to studying the following two initial-boundary value problems for semilinear wave equations with variable coefficients on exterior domain with subcritical exponent in $n$ space dimensions: u_{tt}-partial_{i}(a_{ij}(x)\partial_{j}u)=|u|^{p}, (x,t)\in \Omega^{c}\times(0,+\infty), n\geq 3 and u_{tt}-\partial_{i}(a_{ij}(x)\partial_{j}u)=|u_{t}|^{p}, (x,t)\in \Omega^{c}\times (0,+\infty), n\geq 1, where $a_{ij}(x)=\delta_{ij}, when |x|\geq R. The exponents $p$ satisfies $ 1

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