Asymptotic Behavior of Solutions to a Class of Semilinear Parabolic Equations with Boundary Degeneracy
Year: 2023
Author: Xinxin Jing, Chunpeng Wang, Mingjun Zhou
Communications in Mathematical Research , Vol. 39 (2023), Iss. 1 : pp. 54–78
Abstract
This paper concerns the asymptotic behavior of solutions to one-dimensional semilinear parabolic equations with boundary degeneracy both in bounded and unbounded intervals. For the problem in a bounded interval, it is shown that there exist both nontrivial global solutions for small initial data and blowing-up solutions for large one if the degeneracy is not strong. Whereas in the case that the degeneracy is strong enough, the nontrivial solution must blow up in a finite time. For the problem in an unbounded interval, blowing-up theorems of Fujita type are established. It is shown that the critical Fujita exponent depends on the degeneracy of the equation and the asymptotic behavior of the diffusion coefficient at infinity, and it may be equal to one or infinity. Furthermore, the critical case is proved to belong to the blowing-up case.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2021-0108
Communications in Mathematical Research , Vol. 39 (2023), Iss. 1 : pp. 54–78
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Asymptotic behavior boundary degeneracy blowing-up.
Author Details
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Asymptotic behavior of solutions to multi-dimensional semilinear parabolic equations with general diffusion coefficients
Jing, Xinxin
Wang, Chunpeng
Wang, Xinyue
Journal of Mathematical Analysis and Applications, Vol. 527 (2023), Iss. 1 P.127377
https://doi.org/10.1016/j.jmaa.2023.127377 [Citations: 0]