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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
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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:UNDER REVIEW

13 Nov 2020Submitted to Mathematical Methods in the Applied Sciences
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