Abstract
In this paper the quasilinear heat equation with the nonlinear boundary condition is studied. The blow-up rate and existence of a self-similar solution are obtained. It is proved that the rescaled function v ( y , t ) = ( T − t ) 1 / ( 2 p + α − 2 ) u ( ( T − t ) ( p − 1 ) / ( 2 p + α − 2 ) y , t ) , behaves as t → T like a nontrivial self-similar profile.
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