Self-similar solutions in reaction-diffusion systems
Volume 60 / 2003
Banach Center Publications 60 (2003), 337-346
MSC: Primary 35B40; Secondary 35K55
DOI: 10.4064/bc60-0-26
Abstract
In this paper we examine self-similar solutions to the system $$ \begin{alignedat}2 u_{it} - d_i \Delta u_i &= \prod_{k=1}^{m} u_k^{p_k^i}, \quad&& i=1,\ldots,m , \quad x \in \mathbb R^N , \quad t > 0, \cr u_i(0,x) &= u_{0i}(x) , && i=1,\ldots,m , \quad x \in \mathbb R^N , \end{alignedat} $$ where $m>1$ and $p_k^i>0$, to describe asymptotics near the blow up point.
