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This paper deals with the behavior of positive solutions to the following nonlocal polytropic filtration system with nonlinear boundary conditions and the initial data (u0, v0), where m1,m2 ≥ 1, p1, p2 > 1, l11, l12, l21, l22, q11, q12, q21, q22 > 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. © 2013 The Korean Mathematical Society.

LOCAL AND GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A POLYTROPIC FILTRATION SYSTEM WITH NONLINEAR MEMORY AND NONLINEAR BOUNDARY CONDITIONS