Related papers: An exact solution for the magnetic diffusion probl…
The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…
We present a new method for the approximate solution of the strongly coupled, nonlinear stress-diffusion problem that appears when modeling hydrogen transport in metals. The most salient feature of the proposed approximation is that it is…
In certain astrophysical systems the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the moving-mesh code AREPO. We…
This paper is devoted to the investigation of the backward problem for a multi-term time-fractional diffusion equation. Backward problems for fractional diffusion equations are typically studied using regularization methods due to their…
We obtain a rigorous upper bound on the resistivity $\rho$ of an electron fluid whose electronic mean free path is short compared to the scale of spatial inhomogeneities. When such a hydrodynamic electron fluid supports a non-thermal…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…
We consider a one-dimensional harmonic crystal with conservative noise, in contact with two stochastic Langevin heat baths at different temperatures. The noise term consists of collisions between neighbouring oscillators that exchange their…
This work studies exact solvability of a class of fractional reaction-diffusion equation with the Riemann-Liouville fractional derivatives on the half-line in terms of the similarity solutions. We derived the conditions for the equation to…
In this chapter we consider different approximations for the one-dimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear…
A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk…
We investigate the effect of numerical magnetic diffusion in magnetohydrodynamic simulations of magnetically supported molecular clouds. To this end, we have performed numerical studies on adaptive mesh isothermal simulations of marginally…
Using numerical methods, we systematically study in the framework of ideal MHD the effect of magnetic fields on heat transfer within a turbulent gas. We measure the rates of passive scalar diffusion within magnetized fluids and make the…
This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and…
In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…
The dispersion equation of MGD plasma waves measured in a reference frame with a relative speed from that where they are generated is derived. The analysis leads further from what is known for waves produced in stationary plasmas in the…
The aim of this paper is to provide a comprehensive study of some linear nonlocal diffusion problems in metric measure spaces. These include, for example, open subsets in $\mathbb{R}^N$, graphs, manifolds, multi-structures or some fractal…
The full MHD problem of the flow and heat transfer due to a linearly stretching sheet in the presence of a transverse magnetic field is put in a self-similar form. Traditionally ignored physical processes such as induced magnetic field,…
We consider fast magnetic reconnection that takes place within turbulent magnetic flux and show that the process results in diffusion of magnetic fields and matter, which we term reconnection diffusion. The process of reconnection diffusion…
Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups and discontinuities.…