Global existence and nonexistence for diffusive polytropic filtration equations with nonlinear boundary conditions

Abstract

In this paper, we deal with the global existence and nonexistence of solutions to a diffusive polytropic filtration system with nonlinear boundary conditions. By constructing various kinds of sub-and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of nonnegative solutions, which extend the recent results of Li et al.

Blow-up in the Parablic Problems under Nonlinear Boundary Conditions

“…In particular, many paper have been devoted to study critical exponents of the slow di_usion case (see [2,4,6,8,10,13,22,23,26,29,31,33,34,35] and references therein). Recently, many authors transfer their attention to the fast diffusion case (see [4,8,9,14,15,17,28,32]) and many important results about critical exponents have been obtained. The concept of critical Fujita exponents was proposed by Fujita in the 1960s during discussion of the heat conduction equation with a nonlinear source (see [5]).…”