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Blow-up for the wave equation with nonlinear source and boundary damping terms
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 145 / Issue 4 / August 2015
- Published online by Cambridge University Press:
- 20 July 2015, pp. 759-778
- Print publication:
- August 2015
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- Article
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The paper deals with blow-up for the solutions of an evolution problem consisting in a semilinear wave equation posed in a bounded C1,1 open subset of ℝn, supplied with a Neumann boundary condition involving a nonlinear dissipation. The typical problem studied is
where ∂Ω = Γ0 ∪ Γ1, Γ0 ∩ Γ1 = ∅, σ(Γ0) > 0, 2 < p ≤ 2(n − 1)/(n − 2) (when n ≥ 3), m > 1, α ∈ L∞(Γ1), α ≥ 0 and β ≥ 0. The initial data are posed in the energy space.The aim of the paper is to improve previous blow-up results concerning the problem.
