TY - JOUR
T1 - Asymptotic Behavior of Solutions to a Class of Semilinear Parabolic Equations with Boundary Degeneracy
AU - Jing , Xinxin
AU - Wang , Chunpeng
AU - Zhou , Mingjun
JO - Communications in Mathematical Research 
VL - 1
SP - 54
EP - 78
PY - 2022
DA - 2022/10
SN - 39
DO - http://doi.org/10.4208/cmr.2021-0108
UR - https://global-sci.org/intro/article_detail/cmr/21078.html
KW - Asymptotic behavior, boundary degeneracy, blowing-up.
AB - <p style="text-align: justify;">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.</p>