# American Institue of Mathematical Sciences

1996, 2(4): 483-496. doi: 10.3934/dcds.1996.2.483

## The asymptotic behavior of solutions of a semilinear parabolic equation

 1 Department of Mathematics, Chonnam National University, Kwangju, 500-757, South Korea, South Korea

Received  October 1995 Revised  March 1996 Published  July 1996

We study the long-time behavior of solutions of the Cauchy problem

$u_t=\Delta u - (u^q)_y- u^p, \quad p, q >1,$

defined in the domain $Q=\{ (x, t): x=(x, y) \in \mathbf{R}^{N-1} \times \mathbf{R}, t >0 \}$ with nonnegative initial data in $L^1( \mathbf{R}^N)$. We completely classify the asymptotic profiles of solutions as $t \to \infty$ according to the parameters $p$ and $q$. We use rescaling transformations and a priori estimates.

Citation: Minkyu Kwak, Kyong Yu. The asymptotic behavior of solutions of a semilinear parabolic equation. Discrete & Continuous Dynamical Systems - A, 1996, 2 (4) : 483-496. doi: 10.3934/dcds.1996.2.483
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