loading page

Improving a method of constructing finite time blow-up solutions and its an application
  • QF Long
QF Long
Guizhou Normal University

Corresponding Author:[email protected]

Author Profile

Abstract

We in this paper improve a method of establishing the existence of finite time blow-up solutions, and then apply it to study the finite time blow-up, the blow-up time and the blow-up rate of the weak solutions on the initial boundary problem of u_t - \Delta u_{t} - \Delta u_{t} = |u|^{p - 1}u. By applying this improved method, we prove that I(u_{0}) < 0 is a sufficient condition of the existence of the finite time blow-up solutions and \frac{2(p - 1)^{-1}\|u_{0}\|_{H_{0}^{1}}^{2}}{(p - 1) \|\nabla u_{0}\|_{2}^{2} - 2(p + 1)J(u_{0})} is an upper bound for the blow-up time, which generalize the blow-up results of the predecessors in the sense of the variation. Moreover, we estimate the upper blow-up rate of the blow-up solutions, too.
24 Nov 2020Submitted to Mathematical Methods in the Applied Sciences
25 Nov 2020Submission Checks Completed
25 Nov 2020Assigned to Editor
21 Jun 2021Reviewer(s) Assigned
23 Jun 2021Review(s) Completed, Editorial Evaluation Pending
24 Jun 2021Editorial Decision: Revise Minor
07 Aug 20211st Revision Received
07 Aug 2021Submission Checks Completed
07 Aug 2021Assigned to Editor
13 Oct 2021Reviewer(s) Assigned
03 Nov 2022Review(s) Completed, Editorial Evaluation Pending
04 Nov 2022Editorial Decision: Revise Minor
30 Nov 20222nd Revision Received
30 Nov 2022Submission Checks Completed
30 Nov 2022Assigned to Editor
30 Nov 2022Review(s) Completed, Editorial Evaluation Pending
02 Dec 2022Editorial Decision: Accept
Apr 2023Published in Mathematical Methods in the Applied Sciences volume 46 issue 6 on pages 7305-7310. 10.1002/mma.8971