Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by distributed-order equations. In the present paper we consider different forms of distributed-order fractional kinetic equations and investigate the effects descri...

We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators that are generators of pure jump Lévy processes (e.g. the fractional Laplacian). As an application, we derive continuous dependence estimates on the nonlinea...

The general quasi-linear autonomous fourth order diffusion equation ut = −[G(u)uxxx + h(u, ux, uxx)]x with positive variable diffusivity G(u) and lower-order flux component h is considered on the real line. A direct algorithm produces a general class of equations for which the Shannon entropy density obeys a reaction-diffusion equation with a positive irreducible source term. Such equations may...

in this paper, a non-isothermal two-phase flow in the cathode gas diffusion layer (gdl) of pem fuel cell is modeled. the governing equations including energy, mass and momentum conservation equations are solved by numerical methods. also, the optimal values of the effective parameters such as the electrodes porosity, gas diffusion layer (gdl) thickness and inlet relative humidity are calculated...

Abstract In this work we investigate the well-posed for diffusion equations associated to subelliptic pseudo-differential operators on compact Lie groups. The by strongly elliptic is considered as a special case and in particular fractional with respect Laplacian. general studied within Hörmander classes sub-Riemannian structure group (encoded system of vector fields). Applications sub-Laplacia...

This paper is concerned with the traveling waves for a class of delayed non-local diffusion equations with crossing-monostability. Based on constructing two associated auxiliary delayed non-local diffusion equations with quasi-monotonicity and a profile set in a suitable Banach space using the traveling wave fronts of the auxiliary equations, the existence of traveling waves is proved by Schaud...

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-know...

In this work we present a result on linear diffusion equations with point controls. This is the first partial result obtained along the completion of [5] which includes more general nonlinear diffusion equations. The main focus here is showing how recent variational principles based on Wasserstein metric, used to solve homogeneous diffusion equations, can actually be extended to solving nonhomo...

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton's method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, ...