Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.

The nonlinear coefficients defining the mean electromotive force (i.e., the nonlinear turbulent magnetic diffusion, the nonlinear effective velocity, the nonlinear kappa tensor, etc.) are calculated for an anisotropic turbulence. A particular case of an anisotropic background turbulence (i.e., the turbulence with zero-mean magnetic field) with one preferential direction is considered. It is sho...

This paper proposes new enhancement models to the methods of nonlinear anisotropic diffusion to greatly reduce speckle and preserve image features in medical ultrasound images. By incorporating local physical characteristics of the image, in this case scatterer density, in addition to the gradient, into existing tensorbased image diffusion methods, we were able to greatly improve the performanc...

We study a class of numerical schemes for nonlinear diffusion filtering that offers insights on the design of novel wavelet shrinkage rules for isotropic and anisotropic image enhancement. These schemes utilise analytical or semi-analytical solutions to dynamical systems that result from space-discrete nonlinear diffusion filtering on minimalistic images with 2×2 pixels. We call them locally an...

Abstract. This paper is concerned with the analysis of the discontinuous Galerkin finite element method applied to nonstationary convection-diffusion problems with nonlinear convection and nonlinear diffusion. We generalize results from [2], where linear diffusion is assumed. Optimal error estimates are obtained for the L(H) norm and interelement jump terms, however due to the nonlinearity of t...

A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map. We find that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the control parameter. The measure of these self-similar sets is positive, parameter dependent, and in case of normal diffusion it shows a fractal diffusion coeffi...