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

This paper deals with the behavior of positive solutions to the following nonlocal polytropic filtration system [GRAPHICS] with nonlinear boundary conditions u(x)vertical bar(x=a) = u(q11)v(q12)vertical bar(x=a), v(x)vertical bar(x=0) = 0, v(x)vertical bar(x=a) = u(q21)v(q22)vertical bar(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.