Nonlinear Diffusion 1 Introduction: Motivation for non . . . - UMD Nonlinear Diffusion These notes summarize the way I present this material, for my benefit But everything in here is said in more detail, and better, in Weickert’s paper 1 Introduction: Motivation for non-standard diffusion First, let’s begin with some definitions and examples of why we want to use other kinds of diffusion
Nonlinear Diffusion. Porous Medium and Fast Diffusion. From . . . My group works in the areas of Nonlinear Diffusion and Reaction Diffusion I will present an overview and recent results in the theory mathematically called Nonlinear Parabolic PDEs General formula ut = P ∂iAi(u,∇u) + P B(x,u,∇u) Typical nonlinear diffusion: ut = ∆um Typical reaction diffusion: ut = ∆u+up Juan L Vazquez - Nonlinear
Nonlinear Diffusion - Universiteit van Amsterdam Nonlinear diffusion is an image smoothing technique that is based on the physical notion of diffusion The smoothing can be locally controlled with the diffusion tensor in such a way that in the neighborhood of edges smoothing is less pronounced then in other areas
NON-LINEAR DIFFUSION FILTERING - Chalmers • Non-Linear Diffusion • Reduces noise and enhances contours in images • The diffusion coefficient is locally adapted, becoming negligible as object boundaries are approached • Noise is efficiently removed and object contours are strongly enhanced Image Analysis Group Non-Linear Diffusion Filtering Autumn 2000 Page 4
ADI schemes for higher-order nonlinear diffusion equations Alternating Direction Implicit (ADI) schemes are constructed for the solution of two-dimensional higher-order linear and nonlinear diffusion equations, particularly including the fourth-order thin film equation for surface tension driven fluid flows
Exact solutions of nonlinear diffusion equations by . . . In this paper, we apply VIM to obtain exact solutions of nonlinear diffusion equations in the form (1) u t = (D (u) u x) x subject to the initial condition: (2) u (x, 0) = f (x) where D (u) is the diffusion term, which plays an important role in wide range of applications in the diffusion processes