Doubly nonlinear parabolic equations with singular lower order term

The Hardy inequality and nonlinear parabolic equations on Carnot groups

“…These inequalities play an important role in the study of linear and nonlinear partial differential equations on Euclidean space R n and on the Heisenberg group H n (see [1], [4], [7], [8], [11], [16], [19], [20], [21], [22], [23], [26], [27], [33]). …”

“…The observation of Cabré and Martel [8] used to get additional results on nonexistence of positive solutions for wide class of linear and nonlinear parabolic problems on Euclidean space R n and the Heisenberg group H n ( see [18], [19], [20], [21], [23], [26], and [27]). The purpose of this paper is to investigate nonexistence of positive solutions of the problem(1.1) on more general Carnot group G and our results recover the previous results [20], [21].…”

Nonlinear degenerate parabolic equations for Baouendi–Grushin operators

“…on the Euclidean space and the results were extended to the Heisenberg group [24]. We shall also consider this problem for the Baouendi-Grushin operator in a separate paper [25].…”

Numerical Investigation of Solutions to a Reaction-diffusion System with Variable Density

“…Studying different properties of solutions to system (1) is a complicated problem, even for particular cases of system (1) [2,[6][7][8][9]. In these works for particular cases of system (1)- (2) the effectiveness was shown of the self-similar approach for studying different properties of solutions to problem (1)- (2).…”