Related papers: Weak-strong uniqueness for Maxwell-Stefan systems
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…
We prove strong convergence of an upwind-type finite volume method to a weak solution of the Navier-Stokes-Fourier system with the Dirichlet boundary conditions. The limit solution satisfies a weak form of the mass and momentum equations,…
We consider a diffuse interface model of tumor growth proposed by A.~Hawkins-Daruud et al. This model consists of the Cahn-Hilliard equation for the tumor cell fraction $\varphi$ nonlinearly coupled with a reaction-diffusion equation for…
We investigate linear parabolic equations in divergence form with singular coefficients and non-smooth boundary data. When the diffusion, drift, or potential terms, as well as the initial or boundary conditions, are distributions rather…
In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a…
In this paper we consider the flow of two incompressible, viscous and immiscible fluids in a bounded domain, with different densities and viscosities. This model consists of a coupled system of Navier-Stokes and Mullins-Sekerka type parts,…
An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the multidimensional torus is analyzed. The equations describe the dynamics of population species with repulsive or attractive interactions. The numerical…
In this paper, we study the existence and uniqueness of weak solution of a nonlinear poroelasticity model. To better describe the proccess of deformation and diffusion underlying in the original model, we firstly reformulate the nonlinear…
We construct non-negative weak solutions of fast diffusion equations with a divergence type of drift term satisfying the $L^q$-energy inequality and speed estimate in Wasserstein spaces under some integrability conditions on the drift term.…
In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker-Planck-type equations to the case of nonconstant full diffusion matrices. While in existing works the schemes are…
We introduce the notion of relative entropy for the weak solutions of the compressible Navier-Stokes system. We show that any finite energy weak solution satisfies a relative entropy inequality for any pair of sufficiently smooth test…
The self-diffusion process of a hard sphere fluid confined by two parallel plates separated by a distance on the order of the particle diameter is studied. The starting point is a closed kinetic equation for the distribution function that…
A class of parabolic-parabolic Keller-Segel systems with degenerate diffusion and volume filling is studied in a bounded domain subject to no-flux boundary conditions. The equations are derived from a multiphase fluid model. The interplay…
We consider a (degenerate) cross-diffusion model of tumor growth structured by phenotypic trait. We prove the existence of weak solutions and the incompressible limit as the pressure becomes stiff extending methods recently introduced in…
We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…
In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension - like, for example, the evolution of oil bubbles in water. Our main result is a weak-strong uniqueness principle…
We study a nonlinear branching diffusion process in the sense of McKean, i.e., where particles are subjected to a mean-field interaction. We consider first a strong formulation of the problem and we provide an existence and uniqueness…
Two frameworks that have been used to characterize reflected diffusions include stochastic differential equations with reflection and the so-called submartingale problem. We introduce a general formulation of the submartingale problem for…
The Busenberg--Travis cross-diffusion system for segregating populations is approximated by the compressible Navier--Stokes--Korteweg equations on the torus, including a density-dependent viscosity and drag forces. The Korteweg term can be…
We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and…