Quenching of solutions to a class of semilinear parabolic equations with boundary degeneracy

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:421

Article

Zhou, Mingjun¹  Wang, Chunpeng¹  Nie, Yuanyuan¹ 

[1] Jilin Univ, Sch Math, Changchun 130012, Peoples R China

关键词: Quenching;    Boundary degeneracy;    Critical length;   

DOI  :  10.1016/j.jmaa.2014.06.079

来源: Elsevier

【 摘 要 】

This paper concerns the quenching phenomenon of solutions to a class of semilinear parabolic equations with boundary degeneracy. In the case that the degeneracy is not strong, it is shown that there exists a critical length, which is positive, such that the solution exists globally in time if the length of the spatial interval is less than it, while quenches in a finite time if the length of the spatial interval is greater than it. Whereas in the case that the degeneracy is strong enough, the solution must be quenching in a finite time no matter how long the spatial interval is. Furthermore, for each quenching solution, the set of quenching points is determined and it is proved that its derivative with respect to the time must blow up at the quenching time. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free