Some results for an $${\mathcal{N}}$$-dimensional nonlinear diffusion equation with radial symmetry

Abstract

The solutions of a nonlinear diffusion equation by considering the radially symmetric N-dimensional case are investigated. This equation has the nonlinearity present in the diffusive term and external force. The solutions are obtained by using a similarity method and connected to the q-exponential and q-logarithmic functions which emerge from the Tsallis formalism. In addition, the results obtained here may be useful to investigate a rich class of situations related to anomalous diffusion.

Generalized Fourier Transform Method for Solving Nonlinear Anomalous Diffusion Equations

“…For example, anomalous diffusion can be obtained by the usual Fokker-Planck equation, but with a variable diffusion coefficient [5,6]. It can also be achieved by incorporating nonlinear terms in the diffusion term, or external forces [7][8][9][10]. In some approaches, fractional equations have been employed to analyze anomalous diffusion and related phenomena [11][12][13][14].…”

Solutions and symmetry reductions of the radially symmetric non-Newtonian polytropic filtration equations

“…Equation (4) can be regarded as a natural generalization of the porous medium equation and the p-laplace equation. Some exact solutions, such as similarity solutions, instantaneous source type solutions to certain special forms of (4) have been obtained by the symmetry-related methods including the classical method [32], [33], [34], [35], the conditional symmetry method [9], [36], [37], [38], the CLBS method [11]- [25], the sign-invariant approach [26]- [29] and the ansatz-based method [30], [39], [40] and the similarity method [31]. We shall construct solutions of (4) by means of the approach of CLBS for p = 2 since the CLBS for this special case had been discussed in [15].…”