EXISTENCE AND BLOW-UP OF SOLUTIONS FOR A NON-LOCAL FILTRATION AND POROUS MEDIUM PROBLEM.

We consider a non-local filtration equation of the form u_t = ΔK(u) + λf(u) (∫_Ω f(u) dx)^-p and a porous medium equation, in this case K(u) = u^m, with some boundary and initial data u₀, where 0 < p < 1 and f, f′, f″ > 0. We prove blow-up of solutions for sufficiently large values of the parameter λ > 0 and for any u₀ > 0, or for sufficiently large values of u₀ > 0 and for any λ > 0. [ABSTRACT FROM AUTHOR]