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

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 o...

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Bibliographic Details
Published in:Applicable analysis 2013-09, Vol.92 (9), p.1863-1888
Main Author: Martynenko, A.V.
Format: Article
Language:English
Subjects:
Cauchy problem
Cauchy problems
Density
Estimates
Fujita critical exponent
global existence
inhomogeneous density
Integrals
Linear equations
Mathematical analysis
Parabolas
quasilinear parabolic equation
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Description
Summary: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.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2012.708408