Solutions with moving singularities for a semilinear parabolic equation |
| |
Authors: | Shota Sato Eiji Yanagida |
| |
Institution: | Mathematical Institute, Tohoku University, Sendai 980-8578, Japan |
| |
Abstract: | We consider the Cauchy problem for a semilinear heat equation with power nonlinearity. It is known that the equation has a singular steady state in some parameter range. Our concern is a solution with a moving singularity that is obtained by perturbing the singular steady state. By formal expansion, it turns out that the remainder term must satisfy a certain parabolic equation with inverse-square potential. From the well-posedness of this equation, we see that there appears a critical exponent. Paying attention to this exponent, for a prescribed motion of the singular point and suitable initial data, we establish the time-local existence, uniqueness and comparison principle for such singular solutions. We also consider solutions with multiple singularities. |
| |
Keywords: | Semilinear parabolic equation Critical exponent Moving singularity Cauchy problem |
本文献已被 ScienceDirect 等数据库收录! |
|