Critical exponents of the non-Newtonian polytropic filtration equation with nonlinear boundary condition

Critical exponents for nonlinear diffusion equations with nonlinear boundary sources

“…in various geometries (such as whole space, cones, sectorial domains in R 2 , orthant domains, complement of bounded domains, etc.). We refer to the survey papers [2,15] and references therein, and also the recent papers [5,9,[16][17][18][19][20][21][22]26].…”

Critical curves for a fast diffusive polytropic filtration system coupled via nonlinear boundary flux

“…In particular, many paper have been devoted to study critical exponents of the slow diffusion case (the ranges of parameters m i > 1, p i ≥ 2 or m i ≥ 1, p i > 2), see ( [6], [15], [16], [19], [20]). Recently, many authors transfer their attention to the fast diffusion case (1 < p i < 2 or 0 < m i < 1 or m = 1, p = 2), see ( [3], [6], [7], [9], [11], [17]), and many important results about critical exponents have been obtained.…”

Critical Blow-Up and Extinction Exponents for Non-Newton Polytropic Filtration Equation With Source

“…Recently, a lot of papers are devoted to discuss the following degenerate equation 2) with source and without boundary flux and to reveal the phenomena described as [4], [9]. Following from [2], [8], [11], we can get the local existence of weak solutions in the sense of the following definition.…”