The main theory behind nonlinear diffusion models is to use nonlinear PDEs to create a scale space representation that consists of gradually simplified images where some image features such as edges are maintained or even enhanced. The earliest nonlinear diffusion model proposed in image processing is the so-called anisotropic diffusion1 by Perona and Malik [2]. In their formulation, they repla...

We study the existence and uniqueness of mild strong solutions nonlocal nonlinear diffusion problems $p$-Laplacian type with boundary conditions posed in metric random walk spaces. These spaces include, among others, weighted discrete graphs $\mathbb{R}^N$ a induced by nonsingular kernel. also case dynamical conditions. The generality nonlinearities considered allow us to cover counterparts lar...

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

‎In this paper‎, ‎we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations‎. ‎By a priori estimates‎, ‎difference and variation techniques‎, ‎we establish the existence and uniqueness of weak solutions of this problem.

We develop analytical and numerical tools for the equilibrium solutions of a class of reaction-diffusion models with nonlinear diffusion rates. Such equations arise from population biology and material sciences. We obtain global bifurcation diagrams for various nonlinear diffusion functions and several growth rate functions.

The assessment of image denoising results depends on the respective application area, i.e. image compression, still-image acquisition, and medical images require entirely different behavior of the applied denoising method. In this paper we propose a novel, nonlinear diffusion scheme that is derived from a linear diffusion process in a value space determined by the application. We show that appl...

The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first introduced, and next a regularization scheme is presented. It is shown that the renormalization of an action functional in the generating functional leads to an a...

Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special tools are needed to provide the systematic construction of the nonlinear diffusion equations for multicomponent mixtures with significant interaction between...