The asymptotic behavior of solutions of a semilinear parabolic equation doi:10.3934/dcds.1996.2.483 Abstract Full Text (197.8K) Related Articles
Minkyu Kwak  Department of Mathematics, Chonnam National University, Kwangju, 500757, South Korea (email) Abstract: We study the longtime behavior of solutions of the Cauchy problem $u_t=\Delta u  (u^q)_y u^p, \quad p, q >1,$ defined in the domain $Q=\{ (\x, t): \x=(x, y) \in \mathbf{R}^{N1} \times \mathbf{R}, t >0 \}$ 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.
Keywords: Asymptotic behaviour, a semilinear heat equation, selfsimilar
solution, singular solution.
Received: October 1995; Revised: March 1996; Published: July 1996. 
2013 IF (1 year).923
