Blow-up for the wave equation with nonlinear source and boundary damping terms. Issue 4 (20th July 2015)

• Record Type: Journal Article
• Authors: Fiscella, Alessio; Vitillaro, Enzo
• Is Part Of: Proceedings. Volume 145:Issue 4(2015)
• Page Start: 759
• Page End: 778
• Publication Date: 2015-07-20
• Subjects: wave equation, -- boundary damping, -- blow-up, -- source; Primary 35L05, -- 35L20, -- Secondary 35A01; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210515000165
• Languages: English
• ISSNs: 0308-2105

Abstract

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.