Work

Lifespan estimate for one-dimensional wave equation with semilinear terms of spatial derivative

Year: 2026

Type: article

Abstract: This paper studies the upper and lower bounds of the lifespan for the classical solutions to the initial value problems of one dimensional wave equations with nonautonomous semilinear terms including the space-derivative of the unknown function. This is a nontrivial business comparing to the analogous results with time-derivative type semilinear terms, especially for the proof to obtain the sharp upper bound of the lifespan as we have to deal with space dependent weights among iteration procedures of the weighted functional of the solution. Also it is surprising that a part of them reaches to the same ordinary differential inequality for classical semilinear damped wave equations introduced by Li and Zhou (Discrete Contin. Dynam. Systems, 1995, 1(4): 503–520), and we show a simple proof for blow-up result from this ordinary differential inequality by iteration argument and slicing method in more general situation.

Source: Advances in Nonlinear Analysis

DOI: 10.1515/anona-2025-0200

Authors: Ning-An Lai, Cui Ren, Takiko Sasaki, Hiroyuki Takamura

Institutions: Shaoxing University, Zhejiang Normal University, Musashino University, Tohoku University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,469