UNIVERSAL BOUNDS FOR POSITIVE SOLUTIONS OF DOUBLY DEGENERATE PARABOLIC EQUATIONS WITH A SOURCE

We consider a doubly degenerate parabolic equation with a source term of the form (u(beta))(t) - div(vertical bar del u vertical bar(lambda-1) del u) + u(p) were 0 < beta <= lambda < p. For a positive solution of the equation we prove universal bounds and provide blowup rate estimates under suitable assumptions on p < p(0)(lambda, beta, 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-Weitzenbok formula and local energy estimates.