Related papers: On The Basics of the Nonlinear Diffusion
Non-local equations of motion contain an infinite number of derivatives and commonly appear in a number of string theory models. We review how these equations can be rewritten in the form of a diffusion-like equation with non-linear…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
We generalize the method of obtaining the fundamental linear partial differential equations such as the diffusion and Schrodinger equation, Dirac and telegrapher's equation from a simple stochastic consideration to arrive at certain…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
This paper is concerned with the transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superlinear power-law absorption and a time-independent point…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
In this paper we consider a system of three fractional differential equations describing a nonlinear reaction. Our analysis includes both analytical technique and numerical simulation. This allows us to control the efficiency of the…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
The aim of this article is to study a nonlinear system modeling a Non-Newtonian fluid of polymer aqueous solutions. We are interested here in the existence of weak solutions for the stationary problem in a bounded plane domain or in…
Second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained…
This note is devoted to some nonlocal, nonlinear elliptic problems with an emphasis on the computation of the solution of such problems, reducing it in particular to a fixed point argument in R. Errors estimates and numerical experiments…
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…
We discuss stationary concentrations of reactants in an A + B -> 0 reaction under subdiffusion and show that they are described by stationary reaction-diffusion equations with a nonlinear diffusion term. We consider stationary profiles of…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional…
This paper intends on obtaining the explicit solution of $n$-dimensional anomalous diffusion equation in the infinite domain with non-zero initial condition and vanishing condition at infinity. It is shown that this equation can be derived…