Properties of solutions to porous medium problems with different sources and boundary conditions

Abstract

In this paper we study nonnegative and classical solutions u = u(x, t) to porous medium problems of the typewhere Ω is a bounded and smooth domain of R N , with N ≥ 1, I = (0, t * ) is the maximal interval of existence of u, m > 1 and u 0 (x) is a nonngative and sufficiently regular function. The problem is equipped with different boundary conditions and depending on such boundary conditions as well as on the expression of the source g, global existence and blow-up criteria for solutions to (♦) are established. Additionally, in the three dimensional setting and when blow-up occurs, lower bounds for the blow-up time t * are also derived.2010 Mathematics Subject Classification. 35K55, 35K57, 35A01, 74H35.

Semi-analytical solutions for the diffusive logistic equation with mixed instantaneous and delayed density dependence

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