Critical exponents for porous medium systems coupled via nonlinear boundary flux

Critical Curves for a Coupled System of Fast Diffusive Newtonian Filtration Equations

“…It is clear that the above result is quite different from the known results obtained in [9] for the corresponding one-dimensional problem. By virtue of the radial symmetry of the exterior domain of the unit ball as in [7], the result (1.7) can be extended to the following more general problems: …”

“…In the wake of the pioneering work of Fujita [4], many results on critical Fujita exponents for diffusion equations with nonlinear sources can be found; see [1][2][3][4][5][7][8][9]. It was Ferreira et al [3] who considered the fast diffusive equation with nonlinear boundary sources:…”

“…In [9], the authors studied the coupled system (1.1)-(1.3) in the one-dimensional case, that is, (1.6) with 0 < m, n < 1, p, q ≥ 0. They proved that the critical global existence curve is pq = (m + 1)(n + 1)/4 and the critical Fujita curve is min{α 1 + β 1 , α 2 + β 2 } = 0, where…”

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

“…Xiang ZAMP authors. We note that most of the previous works deal with the special cases such as k = 1 or k = 2 (see [3,7,[11][12][13]18] and reference therein). In particular, Li et al in [13] considered system (1.1)-(1.3) with k = 2 and their results could be summarized as the following proposition (a similar result was obtained independently by Wang et al [18] in the case q i = 2): , then there exists nonglobal solutions to…”

“…The aim of this paper is to give a simple criteria of this classification by using a combination of various kinds of self-similar sub-or super-solutions and the basic properties of the so called M-matrix for general powers m i , indices p ij and number k ≥ 1, which complicate the interaction among various components u i . Paradoxically, our proof is more simple than that of [13,18] in the sense that we do not need some specific computations of parameters in the construction of self-similar sub-or super-solutions, even though we are dealing with an abstract system without specific number k.…”