On Glassey’s conjecture for semilinear wave equations in Friedmann–Lemaître–Robertson–Walker spacetime

Boundary value problems

Yuta Wakasugi¹  Kimitoshi Tsutaya² 

[1] Graduate School of Advanced Science and Engineering, Hiroshima University, 739-8527, Higashi-Hiroshima, Japan;Graduate School of Science and Technology, Hirosaki University, 036-8561, Hirosaki, Japan;

关键词: Wave equation;    Blow-up;    Lifespan;    FLRW spacetime;    Glassey’s conjecture;    35Q85;    35L05;    35L70;   

DOI  :  10.1186/s13661-021-01571-0

来源: Springer

【 摘 要 】

Consider nonlinear wave equations in the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes. We show blow-up in finite time of solutions and upper bounds of the lifespan of blow-up solutions to give the FLRW spacetime version of Glassey’s conjecture for the time derivative nonlinearity. We also show blow-up results for the space derivative nonlinear term.

【 授权许可】

CC BY