Global solvability for quasilinear parabolic equation with inhomogeneous density and a source

Author: Martynenko A.V.  

Publisher: Taylor & Francis Ltd

ISSN: 0003-6811

Source: Applicable Analysis, Vol.92, Iss.9, 2013-09, pp. : 1863-1888

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Abstract

We study the Cauchy problem for quasilinear parabolic equation with inhomogeneous density and a source. We show that this problem has a global solution under the assumptions that initial datum is small enough in the integral sense and the source term has overcritical behaviour. The sharp estimates of a solution is obtained as well.