Global existence and nonexistence of solutions for Newtonian filtration equation. Issue 8 (11th June 2017) - Liu, Changchun; Wang, Huimin
Abstract : In this paper, we study the initial boundary value problem of Newtonian filtration equation in a cone-like do main, where, , with . Let denote the smallest Dirichlet eigenvalue for the Laplace–Beltrami operator on and let l denote the positive root of . We prove that if, then the problem has no global nonnegative solutions for any nonnegative unless ; if, then the problem has global solutions for some .