Blow-up for the wave equation with nonlinear source and boundary damping terms. Issue 4 (20th July 2015) - Fiscella, Alessio; Vitillaro, Enzo
Abstract : The paper deals with blow-up for the solutions of an evolution problem consisting in a semilinear wave equation posed in a bounded C 1, 1 open subset of ℝ n, supplied with a Neumann boundary condition involving a nonlinear dissipation. The typical problem studied is where ∂Ω = Γ 0 ∪ Γ 1, Γ 0 ∪ Γ 1 = ∅, σ ( Γ 0 ) > 0, 2 < p ≤ 2( n − 1)/( n − 2) (when n ≥ 3), m > 1, α ∈ L ∞ ( Γ 1 ), 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.