Editorial Board

JMI2011C-1 Asymptotic behavior of blow-up solutions to a degenerate parabolic equation (pp.1-8)

Author(s): Koichi Anada and Tetsuya Ishiwata

J. Math-for-Ind. 3C (2011) 1-8.

We consider the Dirichlet problems for a degenerate parabolic equation, $u_t=u^{\delta}(\Delta u+\lambda u)$ in a bounded domain in $\mathbb{R}^n$ with a smooth boundary. It has been known that if $\delta \geq 2$ then there exists $u$ which blows up faster than the rate of $(T-t)^{-1/\delta}$, where $T$ is the blow-up time of $u$. The solutions are called "Type 2". In this paper we investigate features for asymptotic behavior of "Type 2" solutions for the case of $\delta=2$ and $\delta>2$.

Keyword(s).  degenerate parabolic equations, blow-up, asymptotic behavior, type 2, eventual monotonicity