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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
For a positive solution of the equation we prove universal bounds and provide blow-up rate estimates under suitable assumptions on p < p0(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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