Related papers: Dirichlet-Neumann Waveform Relaxation Algorithm fo…
In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and…
The paper deals with homogenization of divergence form second order parabolic operators whose coefficients are periodic in spatial variables and random stationary in time. Under proper mixing assumptions, we study the limit behaviour of the…
We consider the two-dimensional advection-diffusion equation on a bounded domain subject to either Dirichlet or von Neumann boundary conditions and study both time-independent and time-periodic cases involving Liouville integrable…
Diffusion probability models have shown significant promise in offline reinforcement learning by directly modeling trajectory sequences. However, existing approaches primarily focus on time-domain features while overlooking frequency-domain…
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an…
We introduce a non-overlapping variant of the Schwarz waveform relaxation algorithm for semilinear wave propagation in one dimension. Using the theory of absorbing boundary conditions, we derive a new nonlinear algorithm. We show that the…
This article studies a dirichlet boundary value problem for singularly perturbed time delay convection diffusion equation with degenerate coefficient. A priori explicit bounds are established on the solution and its derivatives. For…
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.…
Super- and sub- diffusions are two typical types of anomalous diffusions in the natural world. In this work, we discuss the numerical scheme for the model describing the competition between super- and sub- diffusions driven by fractional…
In this work, we theoretically and numerically discuss the time fractional subdiffusion-normal transport equation, which depicts a crossover from sub-diffusion (as $t\rightarrow 0$) to normal diffusion (as $t\rightarrow \infty$). Firstly,…
We consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity…
This paper focuses on a nonlinear convection-diffusion equation with space and time-fractional Laplacian operators of orders $1<\beta<2$ and $0<\alpha\leq1$, respectively. We develop local discontinuous Galerkin methods, including Legendre…
In this paper, we revisit the nonoverlapping domain decomposition methods for solving elliptic problems with high contrast coefficients. Some interesting results are discovered. We find that the Dirichlet-Neumann algorithm and Robin-Robin…
Linear stationary reaction-convection-diffusion equations with Dirichlet boundary conditions are approximated using a simple finite difference method corresponding to central differences and the addition of a high-order stabilization term…
The time-fractional convection-diffusion equation is performed by Lie symmetry analysis method which involves the Riemann-Liouville time-fractional derivative of the order $\alpha\in(0,2)$. In eight cases, the symmetries are obtained and…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…
We propose a new radiation condition for an infinite inhomogeneous two-dimensional medium which is periodic in the vertical direction and remains invariant in the horizontal direction. The classical Rayleigh-expansion radiation condition…
In many models in condensed matter physics and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper…