The nonlinear diffusion equation arises in many important areas of science and technology such as modelling of dopant diffusion in semiconductors. We give analytical solution to N -dimensional radially symmetric nonlinear diffusion equation. The transformation group theoretic approach is applied to analysis of this equation. The one-parameter group transformation reduces the number of independe...

A number of nonlinear phenomena in many branches of sciences such as physical [6], chemical, economical [20] and biological processes [15,14] are described by the interplay of reaction and diffusion or by the interaction between convection and diffusion. One of the well-known partial differential equations (PDEs) which governs a wide variety of them is Burgers equation, which provides the simpl...

Many sensing techniques and image processing applications are characterized by random noisy, or corrupted, image data. Nonlinear Anisotropic diffusion is a popular, and theoretically well understood, technique for enhancing such images.Diffusion approaches however require the selection of an “edge stopping” function, the definition of which is typically adhoc. Many recent techniques for digital...

This Letter describes the theoretical structure of the plasma diffusion layer that develops from an initially sharp gas-metal interface. The layer dynamics under isothermal and isobaric conditions is considered so that only mass diffusion (mixing) processes can occur. The layer develops a distinctive structure with asymmetric and highly nonlinear features. On the gas side of the layer the diffu...

We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators that are generators of pure jump Lévy processes (e.g. the fractional Laplacian). As an application, we derive continuous dependence estimates on the nonlinea...

The concept of product encryption is resident in the majority of symmetric block ciphers. Along with product encryption, two properties were also defined by Shannon, namely diffusion and confusion. In a product cipher such as a Feistel Network (FN), or generally a Substitution Permutation Network (SPN), diffusion is dependent upon two types of primitives, the nonlinear transformation and the sw...

A nonlinear diffusion based image denoising technique is introduced in this paper. The proposed PDE denoising and restoration scheme is based on a novel diffusivity function that uses an automatically detected conductance parameter. A robust mathematical treatment is also provided for our anisotropic diffusion model. We demonstrate that edge-stopping function model is properly chosen, explainin...

A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and convergence analysis are proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection...

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a nonextensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion, and the...