Work

Existence of Solutions of Semilinear Wave Equations With Time‐Dependent Propagation Speed and Time Derivative Nonlinearity

Year: 2026

Type: article

Abstract: ABSTRACT Consider wave equations with time derivative nonlinearity and time‐dependent propagation speed which are generalized versions of the wave equations in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime, the de Sitter spacetime and the anti‐de Sitter space time. We show lower bounds of the lifespan of solutions as well as the global existence by providing an integrability condition on the propagation speed function, which is applicable to the nonlinear wave equation in the expanding FLRW spacetime including the de Sitter spacetime. We also prove that blow‐up in a finite time occurs for the generalized form of the equation in contracting universes such as the anti‐de Sitter spacetime, as well as upper bounds of the lifespan of blow‐up solutions.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.70493

Authors: Kimitoshi Tsutaya, Yuta Wakasugi

Institutions: Hirosaki University, Hiroshima University

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $5,000

Funder: Japan Society for the Promotion of Science