(untitled) (Communications in Mathematical Research, 2021)
In this paper, the authors consider the positive solutions of the system of the evolution p-Laplacian equations cases u_t =div(| ∇u |^p−2 ∇u) + f(u, v), & (x, t) ∈ Ω × (0, T ), & v_t = div(| ∇v |^p−2 ∇v) + g(u, v), & (x, t) ∈ Ω × (0, T) caseswith nonlinear boundary conditions ∂u∂η = h(u, v), ∂v∂η = s(u, v),and the initial data (u_0, v_0), where Ω is a bounded domain in R^n with smooth boundary ∂Ω, p > 2, h(· , ·) and s(· , ·) are positive C^1 functions, nondecreasing in each variable. The authors find conditions on the functions f, g, h, s that prove the global existence or finite time blow-up of positive solutions for every (u_0, v_0).