Local and Global Existence and Blow-Up of Solutions to a Polytropic Filtration System With Nonlinear Memory and Nonlinear Boundary Conditions

Abstract

Abstract. This paper deals with the behavior of positive solutions to the following nonlocal polytropic filtration systemwith nonlinear boundary conditions ux| x=0 = 0, ux|x=a = u q 11 v q 12 |x=a, vx| x=0 = 0, vx|x=a = u q 21 v q 22 |x=a and the initial data (u 0 , v 0 ), where m 1 , m 2 ≥ 1, p 1 , p 2 > 1, l 11 , l 12 , l 21 , l 22 , q 11 , q 12 , q 21 , q 22 > 0. Under appropriate hypotheses, the authors establish local theory of the solutions by a regularization method and prove that the solution either exists globally or blows up in finite time by using a comparison principle.