On a class of nonlocal porous medium equations of Kirchhoff type

We study the Dirichlet problem for the degenerate parabolic equation of the Kirchhoff type (Formula Presented), where p ≥ 2, T > 0, Ω ⊂ Rⁿ, n ≥ 2, is a smooth bounded domain. The coefficient a(·) is real-valued function defined on R₊ and b(·, ·, τ ) is a measurable function with variable nonlinearity in τ. We prove existence of weak solutions of the considered problem under appropriate and general conditions on a and b.