Asymptotic Behavior of Solutions to a Class of Semilinear Parabolic Equations with Boundary Degeneracy  

作　　者：Xinxin Jing Chunpeng Wang Mingjun Zhou 

机构地区：[1]School of Mathematics,Jilin University,Changchun 130012,China

出　　处：《Communications in Mathematical Research》2023年第1期54-78,共25页数学研究通讯（英文版）

基　　金：This work was supported by the National Key R&D Program of China(Grant No.2020YFA0714i01);by the National Natural Science Foundation of China(Grant No.11925105).

摘　　要：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 inter-val,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 solu-tion 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.

关 键 词：Asymptotic behavior boundary degeneracy BLOWING-UP 

分 类 号：O175.26[理学—数学] O231[理学—基础数学]