Blow-up and nonexistence of solutions of some semilinear degenerate parabolic equations

Boundary value problems

Hui Wu¹ 

[1] School of Science, Nanjing University of Science and Technology, Nanjing, P.R. China

关键词: degenerate parabolic equation;    blow-up;    nonexistence;    35K57;    35K65;    35K70;   

DOI  :  10.1186/s13661-015-0423-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper we study a class of semilinear degenerate parabolic equations arising in mathematical finance and in the theory of diffusion processes. We show that blow-up of spatial derivatives of smooth solutions in finite time occurs to initial boundary value problems for a class of degenerate parabolic equations. Furthermore, nonexistence of nontrivial global weak solutions to initial value problems is studied by choosing a special test function. Finally, the phenomenon of blow-up is verified by a numerical experiment.

【 授权许可】

CC BY