Blow-up of solutions for discrete semilinear wave equation with the scale-invariant damping

2025/10/01 by Koji Wada, Wada, Koji, Kyouhei Wakasa +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2510.00439

openalex publication_date 2025/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the blow-up problem for discretized scale-invariant nonlinear dissipative wave equations. It is known that the critical exponents for undiscretized equations (continuous equations) are given by Fujita and Strauss exponents depending on the space dimensions. Our purpose is to obtain results for the discretized equations that correspond to those shown for the continuous one. The proof is based on Matsuya [6], who showed the blow-up problem for discrete semilinear wave equations without dissipative terms, and we found that the result is sharp in the case of one and two space dimensions compared to the continuous equations.

Citations

• The blow-up theorem of a discrete semilinear wave equation

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