Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11010174 | Journal of Mathematical Analysis and Applications | 2019 | 23 Pages |
Abstract
In this paper, we study the initial-boundary value problem for infinitely degenerate semilinear parabolic equations with logarithmic nonlinearity utââ³Xu=ulogâ¡|u|, where X=(X1,X2,â¯,Xm) is an infinitely degenerate system of vector fields, and â³X:=âj=1mXj2 is an infinitely degenerate elliptic operator. Using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, by the Galerkin method and the logarithmic Sobolev inequality, we obtain the global existence and blow-up at +â of solutions with low initial energy or critical initial energy, and we also discuss the asymptotic behavior of the solutions.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Hua Chen, Huiyang Xu,