We prove here an existence result for solutions for a parabolic equation, with non local coefficients arising in image processing. An image is a bounded function u : D → R defined on a rectangular region D. If the function u is not regular, the image is noisy and it is not possible to use it directly in applications, but is necessary to smooth it by means of a nonlinear evolution problem, with ...

An efficient method for scalar advection is developed that selectively preserves monotonicity. Monotonicity preservation is applied only where the scalar field is likely to contain discontinuities as indicated by significant grid-cell-to-grid-cell variations in a smoothness measure conceptually similar to that used in weighted essentially non-oscillatory (WENO) methods. In smooth regions, the n...

We construct a sequence of functions that uniformly converge (on compact sets) to the price of Asian option, which is written on a stock whose dynamics follows a jump diffusion, exponentially fast. Each of the element in this sequence solves a parabolic partial differential equation (not an integro-differential equation). As a result we obtain a fast numerical approximation scheme whose accurac...

We present a detailed analytical and numerical analysis of the nuclear spin dynamics in parabolic quantum wells. The shallow potential of parabolic quantum wells permits substantial modification of the electronic wave function in small electric fields. The nuclear spin relaxation via the hyperfine interaction depends on the electronic local density of states, therefore the local nuclear relaxat...

Transient diffusion equations arise in many branches of engineering and applied sciences (e.g., heat transfer and mass transfer), and are parabolic partial differential equations. It is well-known that, under certain assumptions on the input data, these equations satisfy important mathematical properties like maximum principles and the non-negative constraint, which have implications in mathema...

We consider a system of interacting diffusions on the integer lattice. By letting the mesh size go to zero and by using a suitable scaling, we show that the system converges (in a strong sense) to a solution of the stochastic heat equation on the real line. As a consequence, we obtain comparison inequalities for product moments of the stochastic heat equation with different nonlinearities.

We study existence and stability of travelling waves for nonlinear convection diffusion equations in the 1-D Euclidean space. The diffusion coefficient depends on the gradient in analogy with the p-Laplacian and may be degenerate. Unconditional stability is established with respect to initial data perturbations in L(R). Running head: Poincaré inequality and P.-S. condition

Motivated by diffusion processes on metric graphs and ramified spaces, we consider an abstract setting for interface problems with coupled dynamic boundary conditions belonging to a quite general class. Beside well-posedness, we discuss positivity, L∞-contractivity and further invariance properties. We show that the parabolic problem with dynamic boundary conditions enjoy these properties if an...

Our aim in this article is to construct exponential attractors for singularly perturbed damped wave equations that are continuous with respect to the perturbation parameter. The main difficulty comes from the fact that the phase spaces for the perturbed and unperturbed equations are not the same; indeed, the limit equation is a (parabolic) reaction-diffusion equation. Therefore, previous constr...

In this paper, we solve two problems for some nonlinear SPDE driven by FiskStratonovich stoachastic integral. The main assumption is the commuting property of the drift and diffusion vector fields with respect of the Lie bracket. In the first problem (P1) we construct a classical solution for some nonlinear SPDE of parabolic type by assuming the compatibilty condition concerning the mentioned v...