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RD-systems with chemotaxis: global existence, boundedness and blow-up of solutions
  • Xue Xu,
  • Zhong Huang
Xue Xu
Haerbin University

Corresponding Author:[email protected]

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Zhong Huang
nan kai da xue
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Abstract

result shows that the blow-up is equivalent to the blow-up of the $L^r-$norms of the solutions for $r$ exceeding some critical value $r_c.$ Under very loose conditions we give the estimation of $r_c,$ relying on a variant of Gagliardo-Nirenberg inequality, and a kind of bootstrap method which is very similar to the Alikakos-Moser iteration procedure.
09 Mar 2021Submitted to Mathematical Methods in the Applied Sciences
09 Mar 2021Submission Checks Completed
09 Mar 2021Assigned to Editor
15 Mar 2021Reviewer(s) Assigned
19 Apr 2021Review(s) Completed, Editorial Evaluation Pending
08 Jul 2021Editorial Decision: Revise Minor
19 Aug 20211st Revision Received
19 Aug 2021Submission Checks Completed
19 Aug 2021Assigned to Editor
24 Aug 2021Reviewer(s) Assigned
08 Sep 2021Review(s) Completed, Editorial Evaluation Pending
29 Sep 2021Editorial Decision: Accept
24 Nov 2021Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.7937