Related papers: Lower Bounds for the Advection-Hyperdiffusion Equa…
This paper is concerned with optimal time-decay estimates of solutions of the Cauchy problem to a model system of the radiating gas in $\mathbb{R}^n$. Compared to Liu and Kawashima (2011) \cite{Liu1} and Wang and Wang (2009) \cite{Wang},…
Pseudo-parabolic equations have been used to model unsaturated fluid flow in porous media. In this paper it is shown how a pseudo-parabolic equation can be upscaled when using a spatio-temporal decomposition employed in the…
This paper is concerned with the numerical solution of porous-media flow and transport problems , i. e. heterogeneous, advection-diffusion problems. Its aim is to investigate numerical schemes for these problems in which different time…
We present a novel approach to solve the advection-diffusion equation under arbitrary transporting fields using a quantum-inspired 'Schrodingerisation' technique for Hamiltonian simulation. Although numerous methods exist for solving…
In this paper, we study the cubic defocusing nonlinear wave equation on the three dimensional hyperbolic space. We use the Fourier truncation method to show that the equation is globally well-posed and scatters if the initial data lies in…
In this paper, we derive two bound-preserving and mass-conserving schemes based on the fractional-step method and high-order compact (HOC) finite difference method for nonlinear convection-dominated diffusion equations. We split the…
We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…
We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…
Dispersive and Strichartz estimates for solutions to general strictly hyperbolic partial differential equations with constant coefficients are considered. The global time decay estimates of $L^p-L^q$ norms of propagators are obtained, and…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we solve analytically a one-dimensional fractional diffusion-advection equation for the particle density. We…
We study the long-time behaviour of solutions to the Hardy-Sobolev parabolic equation in critical function spaces for any spatial dimension $d \geq 5$. By employing the Fourier splitting method, we establish precise decay rates for…
This paper aims to determine the initial conditions for quasi-linear hyperbolic equations that include nonlocal elements. We suggest a method where we approximate the solution of the hyperbolic equation by truncating its Fourier series in…
In this paper, we derive decay rates for solutions to the incompressible Navier-Stokes equations and Hall-magnetohydrodynamic equations. We first improve the decay rate of weak solutions to these equations by refining the Fourier splitting…
The aim of this paper is to study and classify the multiplicity of distinguished limits and asymptotic solutions for the advection equation with a general oscillating velocity field with the systematic use of the two-timing method. Our…
This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier Transformation in time, the method utilizes a fixed…
Two Hybridizable Discontinuous Galerkin (HDG) schemes for the solution of Maxwell's equations in the time domain are presented. The first method is based on an electromagnetic diffusion equation, while the second is based on Faraday's and…
This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction-diffusion process. Such systems are especially challenging for model order reduction since the transport cannot be…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
We consider solutions to the 2d Navier-Stokes equations on $\mathbb{T}\times\mathbb{R}$ close to the Poiseuille flow, with small viscosity $\nu>0$. Our first result concerns a semigroup estimate for the linearized problem. Here we show that…