Asymptotical self-similarity in nonlinear parabolic systems

We prove that blowing up solutions of the system

$u_{{it}} - d_{i} \Delta u_{i} = {\prod\limits_{k = 1}^m {u_{k} ^{{p_{k} ^{i} }} ,} }\quad i = 1, \ldots ,m,x \in \mathbb{R}^{N} ,t > 0,$u_{{it}} - d_{i} \Delta u_{i} = {\prod\limits_{k = 1}^m {u_{k} ^{{p_{k} ^{i} }} ,} }\quad i = 1, \ldots ,m,x \in \mathbb{R}^{N} ,t > 0,
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