ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE



Vol. LXXX, 2 (2011)
p. 229 - 242
Universal bounds for positive solutions of doubly degenerate parabolic equations with a source

A. F. Tedeev

Received: August 28, 2010;   Accepted: March 21, 2011


Abstract.   We consider a doubly degenerate parabolic equation with a source term of the form

strom

For a positive solution of the equation we prove universal bounds and provide blow-up rate estimates under suitable assumptions on p 0(λ, β, N). In particular, we extend some of the recent results by K. Ammar and Ph. Souplet concerning the blow-up estimates for porous media equations with a source. Our proofs are based on a generalized version of the Bochner-Weitzenbök formula and local energy estimates.

Keywords:  Degenerate parabolic equations; blow-up; universal bounds.  

AMS Subject classification: Primary:  35K55, 35K65, 35B33 


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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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