相关论文: Anomalous diffusion with absorption: Exact time-de…
We investigate diffusion equations which have concentration dependent diffusion coefficients with physically two relevant Ans\"atze, the self-similar and the traveling wave Ansatz. We found that for power-law concentration dependence some…
The nonlinear diffusion equation $\frac{\partial \rho}{\partial t}=D \tilde{\Delta} \rho^\nu$ is analyzed here, where $\tilde{\Delta}\equiv \frac{1}{r^{d-1}}\frac{\partial}{\partial r} r^{d-1-\theta} \frac{\partial}{\partial r}$, and $d$,…
We consider classical solutions to the kinetic Fokker-Planck equation on a bounded domain $\mathcal O \subset~\mathbb{R}^d$ in position, and we obtain a probabilistic representation of the solutions using the Langevin diffusion process with…
Some fractional and anomalous diffusions are driven by equations involving fractional derivatives in both time and space. Such diffusions are processes with randomly varying times. In representing the solutions to those diffusions, the…
Mass transport problems are ubiquitous in diverse fields of physics and engineering. With the development of fractional calculus, many have taken to studying problems of fractional mass transport either through numerical simulations or…
A nonlinear diffusion equation is proposed to account for thermalization in fermionic and bosonic systems through analytical solutions. For constant transport coefficients, exact time-dependent solutions are derived through nonlinear…
Anomalous (or non-Fickian) diffusion has been widely found in fluid reactive transport and the traditional advection diffusion reaction equation based on Fickian diffusion is proved to be inadequate to predict this anomalous transport of…
This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain…
The time-asymptotic behavior of undamped, nonlinear oscillators with a random frequency is investigated analytically and numerically. We find that averaged quantities of physical interest, such as the oscillator's mechanical energy,…
Fractional diffusion equations imply non-Gaussian distributions that generalise the standard diffusive process. Recent advances in fractional calculus lead to a class of new fractional operators defined by non-singular memory kernels,…
We prove global existence, uniqueness and regularity of the mild, Lp and classical solution of a non-linear Fokker-Planck equation arising in an adaptive importance sampling method for molecular dynamics calculations. The non- linear term…
We prove a Harnack inequality for positive solutions of a parabolic equation with slow anisotropic spatial diffusion. After identifying its natural scalings, we reduce the problem to a Fokker-Planck equation and construct a self-similar…
We study the Fokker-Planck diffusion equation with diffusion coefficient depending periodically on the space variable. Inside a periodic array of inclusions the diffusion coefficient is reduced by a factor called the diffusion magnitude. We…
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…
In inhomogeneous environments, the correct expression of the diffusive flux is often not given by the Fick's law $\Gamma = - D \nabla n $. The most general hydrodynamic equation modelling diffusion is indeed the Fokker-Planck Equation…
We prove existence and uniqueness of the branch of the so-called \emph{anomalous eternal solutions} in exponential self-similar form for the subcritical fast-diffusion equation with a weighted reaction term $$ \partial_tu=\Delta…
We consider the homogenization of a model of reactive flows through periodic porous media involving a single solute which can be absorbed and desorbed on the pore boundaries. This is a system of two convection-diffusion equations, one in…
We provide closed form solutions for an equation which describes the transport of turbulent kinetic energy in the framework of a turbulence model with a single equation.
This work studies nonnegative solutions for the Cauchy, Neumann, and Dirichlet problems of a logistic type reaction-diffusion equation. The finite time blowup results for nonnegative solutions under various restrictions on the coefficients…
We discuss diffusion of particles in a spatially inhomogeneous medium. From the microscopic viewpoint we consider independent particles randomly evolving on a lattice. We show that the reversibility condition has a discrete geometric…