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

Peer review status:UNDER REVIEW

09 Mar 2021Submitted to Mathematical Methods in the Applied Sciences
09 Mar 2021Assigned to Editor
09 Mar 2021Submission Checks Completed
15 Mar 2021Reviewer(s) Assigned
19 Apr 2021Review(s) Completed, Editorial Evaluation Pending