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On critical exponents for weak solutions to the Cauchy problem for one nonlinear equation with gradient non-linearity
  • Maxim Korpusov,
  • Alexandra Matveeva
Maxim Korpusov
Lomonosov Moscow State University Faculty of Physics

Corresponding Author:korpusov@gmail.com

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Alexandra Matveeva
Moscow State University
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Abstract

In this paper, we consider the Cauchy problem for one nonclassical, third-order, partial differential equation with gradient non-linearity $|\nabla u(x,t)|^q$. The solution to this problem is understood in a weak sense. We show that for $1“3/2$ the existence of the only local-in-time weak solution of Cauchy’s problem.If $3/2”

Peer review status:ACCEPTED

13 Nov 2020Submitted to Mathematical Methods in the Applied Sciences
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16 Nov 2020Submission Checks Completed
16 Nov 2020Assigned to Editor
30 Nov 2020Reviewer(s) Assigned
22 Mar 2021Review(s) Completed, Editorial Evaluation Pending
01 Apr 2021Editorial Decision: Revise Minor
23 Apr 20211st Revision Received
24 Apr 2021Submission Checks Completed
24 Apr 2021Assigned to Editor
28 Apr 2021Reviewer(s) Assigned
29 Jun 2021Editorial Decision: Revise Minor
03 Jul 20212nd Revision Received
03 Jul 2021Submission Checks Completed
03 Jul 2021Assigned to Editor
11 Jul 2021Reviewer(s) Assigned
13 Apr 2022Review(s) Completed, Editorial Evaluation Pending
14 Apr 2022Editorial Decision: Revise Major
22 May 20223rd Revision Received
23 May 2022Submission Checks Completed
23 May 2022Assigned to Editor
29 May 2022Review(s) Completed, Editorial Evaluation Pending
30 May 2022Editorial Decision: Revise Minor
08 Jul 20224th Revision Received
09 Jul 2022Submission Checks Completed
09 Jul 2022Assigned to Editor
14 Jul 2022Review(s) Completed, Editorial Evaluation Pending
15 Jul 2022Editorial Decision: Accept