loading page

Fujita blow-up phenomena of solutions for a Dirichlet problem of parabolic equations with space-time coefficients
  • Jiaqi Liu,
  • Fengjie Li,
  • Bingchen Liu
Jiaqi Liu
China University of Petroleum Huadong
Author Profile
Fengjie Li
China University of Petroleum Huadong
Author Profile
Bingchen Liu
College of Science, China University of Petroleum
Author Profile

Abstract

This paper deals with a homogeneous Dirichlet initial-boundary problem of parabolic equations with different space-time coefficients, $$u_t =\Delta u + t^{\sigma_1} u^{\alpha} + \langle x\rangle^{n} v^{p},\quad v_t =\Delta v + \langle x\rangle^{m} u^{q} + t^{\sigma_2} v^{\beta},$$ where the eight exponents are nonnegative constants and $\langle x\rangle$ is the Japanese brackets. We obtain the Fujita exponents of solutions, which are determined by the eight exponents and the dimension of the space domain. Moreover, simultaneous or non-simultaneous blow-up of the two components of blow-up solutions is discussed with or without conditions on the initial data.

Peer review status:UNDER REVIEW

12 May 2021Submitted to Mathematical Methods in the Applied Sciences
12 May 2021Assigned to Editor
12 May 2021Submission Checks Completed
17 May 2021Reviewer(s) Assigned