We employ a nonlinear anisotropic di usion operator like the ones used as a means of ltering and edge enhancement in image processing, in numerical methods for conservation laws. It turns out that algorithms currently used in image processing are very well suited for the design of nonlinear higher-order dissipative terms. In particular, we stabilize the well-known Lax-Wendro formula by means of...

We present a corrected operator splitting COS method for solving nonlinear parabolic equations of convection di usion type The main feature of this method is the ability to correctly resolve nonlinear shock fronts for large time steps as opposed to standard operator splitting OS which fails to do so COS is based on solving a conservation law for modeling convection a heat type equation for mode...

Tritium behavior in plasma-facing components (PFCs) of future tokamak reactors such as ITER is an essential factor in evaluating and choosing the ideal plasma-facing materials (PFMs). One important parameter that in ̄uences tritium buildup and release in candidate materials is the e€ect of material porosity on tritium di€usion and retention. Di€usion in porous materials, for example, consists of...

A transformation is introduced to e!ectively remove level e!ects, i.e. the state dependency of the di!usion function, in a restricted class of multivariate stochastic di!erential equations such that the general continuous}discrete-time nonlinear "ltering problem may be solved using new or existing implementations of the extended kalman "lter (EKF). An implementation of a quasi-maximum likelihoo...

In this paper we consider the pair di usion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two dimensional case. The model includes a nonlinear system of reaction{ drift{di usion equations, a nonlinear ordinary di erential equatio...

We establish L convergence of a viscous splitting method for nonlinear possibly strongly degenerate convection-di usion problems. Since we allow the equations to be strongly degenerate, solutions can be discontinuous and they are not, in general, uniquely determined by their data. We thus consider entropy weak solutions realized by the vanishing viscosity method. This notion is broad enough to ...

In this paper, we study the asymptotic behavior of weak entropy solutions to the Cauchy problem of the so-called p-system with damping. The convergence rates to nonlinear di®usion waves are obtained. The analysis is based on the viscosity method and energy method.

Grayscale error di usion introduces nonlinear distortion (directional artifacts and false textures), linear distortion (sharpening), and additive noise. In color error di usion what color to render is a major concern in addition to nding optimal dot patterns. This article presents a survey of key methods for artifact reduction in grayscale and color error di usion. The linear gain model by Kite...

Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the di usion coefcient. The proofs are based on anisotropic estimates in tangential and normal directions, a...

In certain polymer penetrant systems the e ects of Fickian di usion are dominated by nonlinear viscoelastic behavior Consequently such systems often exhibit concentration fronts unlike those seen in classical Fickian systems These fronts not only are sharper than in standard systems but also propagate at constant speed The mathematical model presented is a moving boundary value problem where th...