Existence and nonexistence of global solutions of some nonlocal degenerate parabolic equations

AbstractThis paper investigates the global existence and nonexistence of positive solutions of the nonlinear degenerate parabolic equation μt = f (μu) (Δμ + a ʃωμ dx) with a homogeneous Dirichlet boundary condition. It is proved that there exists no global positive solution if and only if ʃ 1/(sf(s)) ds < ∞ and ʃωϕ(x) dx >/a, where ϕ(x) is the unique positive solution of the linear elliptic problem −Δϕ(x) = 1, x ∈ Ω; ϕ(x) = 0, x ∈ ∂