A condition for blow-up solutions to discrete semilinear wave equations on networks. Issue 6 (13th April 2022)

• Record Type: Journal Article
• Authors: Choi, Min-Jun
• Is Part Of: Applicable analysis. Volume 101:Issue 6(2022)
• Page Start: 2008
• Page End: 2018
• Publication Date: 2022-04-13
• Subjects: Semilinear wave equations -- discrete Laplacian -- blow-up -- concavity method; 35L05 -- 35L10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1798414
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we consider discrete semilinear wave equations 1 u t t x, t = Δ ω u x, t + f u x, t, x, t ∈ S × 0, + ∞, u x, t = 0, x, t ∈ ∂ S × 0, + ∞, u x, 0 = u 0 x, u t x, 0 = v 0 x, x ∈ S, where S is a network with boundary ∂ S . The main contribution of this work is to introduce a condition 2 ( C ) α ∫ 0 u f s d s ≤ u f ( u ) + β u 2 + γ, u ∈ R, for some α > 2 and β, γ ≥ 0 with 0 ≤ β ≤ α − 2 λ 0 / 2, where λ 0 is the first eigenvalue of discrete Laplacian Δ ω, and we use the concavity method to obtain the blow-up solutions to the above equations.