Some blow-up problems for a semilinear parabolic equation with a potential |
| |
Authors: | Ting Cheng |
| |
Affiliation: | Department of Mathematics, Huazhong Normal University, Wuhan 430079, PR China |
| |
Abstract: | The blow-up rate estimate for the solution to a semilinear parabolic equation ut=Δu+V(x)|u|p−1u in Ω×(0,T) with 0-Dirichlet boundary condition is obtained. As an application, it is shown that the asymptotic behavior of blow-up time and blow-up set of the problem with nonnegative initial data u(x,0)=Mφ(x) as M goes to infinity, which have been found in [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006], is improved under some reasonable and weaker conditions compared with [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006]. |
| |
Keywords: | Blow-up rate Blow-up time Blow-up set Semilinear parabolic equations Potential |
本文献已被 ScienceDirect 等数据库收录! |
|