相关论文: Coupled transport equations with freezing

We investigate the mixing properties of solutions to the stochastic transport equation $d u= \circ d W \cdot\nabla u$, where the driving noise $W(t,x)$ is white in time, colored and divergence-free in space. Furthermore, we prove the…

Freezing of simple liquid metals and the relative stabilities of competing crystalline solids are investigated using thermodynamic perturbation theory, the interactions between ions being modeled by effective pair potentials derived from…

Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…

We introduce the concept of transport waves by showing that the linearized Boltzmann transport equation admits excitations in the form of waves that have well defined dispersion relations and decay times. Crucially, these waves do not…

A plasma transport theory that spans weak to strong coupling is developed from a binary collision picture, but where the interaction potential is taken to be an effective potential that includes correlation effects and screening…

We study the existence and stability of periodic traveling-wave solutions for complex modified Korteweg-de Vries equation. We also discuss the problem of uniform continuity of the data-solution mapping.

We prove existence of weak solutions of the 3D compressible semi-geostrophic (SG) equations with compactly supported measure-valued initial data. These equations model large-scale atmospheric flows. Our proof uses a particle discretisation…

In this note, we investigate a doubly nonlinear diffusion equation in the slow diffusion regime. We prove stability of the pressure of solutions that are close to traveling wave solutions in a homogeneous Lipschitz sense. We derive…

A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…

Water usually contains dissolved gases, and because freezing is a purifying process these gases must be expelled for ice to form. Bubbles appear at the freezing front and are then trapped in ice, making pores. These pores come in a range of…

Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…

Transport properties of a suspension of solid particles in a viscous gas are studied. The dissipation in such systems arises from two sources: inelasticity in particle collisions and viscous dissipation due to the effect of the gas phase on…

Ultracold condensates provide a unique platform for exploring soliton physics. Motivated by the recent experiments realizing the sine-Gordon model in a split one-dimensional (1D) BEC, we demonstrate that this system naturally supports…

We study an inhomogeneous coagulation equation that contains a transport term in the spatial variable modeling the sedimentation of clusters. We prove local existence of mass conserving solutions for a class of coagulation kernels for which…

We introduce a multivariate version of causal transport, which we name multicausal transport, involving several filtered processes among which causality constraints are imposed. Subsequently, we consider the barycenter problem for…

We consider an isothermal gas flowing through a straight pipe and study the effects of a two-way electronic valve on the flow. The valve is either open or closed according to the pressure gradient and is assumed to act without any time or…

In this paper we propose local and global existence results for the solution of systems characterized by the coupling of ODEs and PDEs. The coexistence of distinct mathematical formalisms represents the main feature of hybrid approaches, in…

We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and…

We study a class of elliptic competition-diffusion systems of long range segregation models for two and more competing species. The existence and uniqueness of the solution are shown. We prove that as the competition rate goes to infinity…

A Hamilton-Jacobi equation with Caputo's time-fractional derivative of order less than one is considered. The notion of a viscosity solution is introduced to prove unique existence of a solution to the initial value problem under periodic…