The blow-up theorem of a discrete semilinear wave equation

2011/07/11 by Keisuke Matsuya, Matsuya, Keisuke · 2 citations
Mathematics · Physics and Astronomy · #35B44 #35L71 #39A12 #39A14 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1107.1917

openalex publication_date 2011/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equation has solutions which show characteristics corresponding to the characteristics of the blow-up solutions for the original equation. The initial value problem for the original equation has blow-up solutions when a certain condition is met. We prove that when a similar condition as that of the original solution is met in the initial value problem for the introduced difference equation, the introduced difference equation has blow-up solutions having characteristics corresponding to the characteristics of the blow-up solutions for the original equation.

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• A revisit on the critical blow-up for semilinear wave equations in low space dimensions with slicing method
• Blow-up of solutions for discrete semilinear wave equation with the scale-invariant damping

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