Global existence and blow-up for a non-Newton polytropic filtration system with nonlocal source

Abstract

This paper deals the global existence and blow-up properties of the following non-Newton polytropic filtration system with nonlocal source, u t-δm,p u=a ∫ Ω να (x,t)dx, vt-Δn,q ν=b ∫Ω uβ(x,t)dx. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time depending on the initial data and the relations between αβ and mn(p-1)(q-1). In the special case, α=n(q-1), β=m(p-1), we also give a criteria for the solution to exist globally or blow up in finite time, which depends on a,b and χ(x),ν(x) as defined in our main results. Copyright © Australian Mathematical Society 2009.