Abstract
In this paper we consider the Cauchy problem of semilinear parabolic equations with nonlinear gradient terms a ( x ) | u | q − 1 u | ∇ u | p . We prove the existence of global solutions and self-similar solutions for small initial data. Moreover, for a class of initial data we show that the global solutions behave asymptotically like self-similar solutions as t → ∞ .
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