Related papers: On weak closure of some diffusion equations
This paper is concerned with approximations of the Boltzmann equation based on the method of moments. We propose a generalization of the setting of the moment-closure problem from relative entropy to {\phi}-divergences and a corresponding…
The existence of weak solutions to the continuous coagulation equation with multiple fragmentation is shown for a class of unbounded coagulation and fragmentation kernels, the fragmentation kernel having possibly a singularity at the…
A note on the property of weak contraction, which implies that all bounded solutions of a nonlinear system converge to a (possibly non-unique) equilibrium. We provide some simple results about interconnections of such systems, and a brief…
We prove that various notions of supersolutions to the porous medium equation are equivalent under suitable conditions. More spesifically, we consider weak supersolutions, very weak supersolutions, and $m$-superporous functions defined via…
A number of methods are discussed which may serve for a treatment of electron correlations in solids. When the electron correlations are relatively weak like in semiconductors or a number of ionic crystals one may start from a…
High-order accurate, $\textit{entropy stable}$ numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space…
In this paper, we prove a large deviation principle for the empirical measures of a system of weakly interacting diffusion with reflection. We adopt the weak convergence approach. To make this approach work, we show that the sequence of…
In this article, we study the passage of limits from discrete to continuous condensing aggregation equation which comprises of Oort-Hulst-Safronov (OHS) equation together with inverse aggregation process. We establish the relation between…
Conserving approximations are applied to the attractive Holstein and Hubbard models (on an infinite-dimensional hypercubic lattice). All effects of nonconstant density of states and vertex corrections are taken into account in the…
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
We consider a system of partial differential equations which describes steady flow of a compressible heat conducting chemically reacting gaseous mixture. We extend the result from Giovangigli, Pokorn\'y, Zatorska (2015) in the sense that we…
We derive a diffusion approximation for the kinetic Vlasov-Fokker-Planck equation in bounded spatial domains with specular reflection type boundary conditions. The method of proof involves the construction of a particular class of test…
We prove a contraction in $L^1$ property for the solutions of a nonlinear reaction--diffusion system whose special cases include intercellular transport as well as reversible chemical reactions. Assuming the existence of stationary…
This paper explores the well known approximation approach to decide weak bisimilarity of Basic Parallel Processes. We look into how different refinement functions can be used to prove weak bisimilarity decidable for certain subclasses. We…
This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…
In this paper we study higher order weakly hyperbolic equations with time dependent non-regular coefficients. The non-regularity here means less than H\"older, namely bounded coefficients. As for second order equations in \cite{GR:14} we…
In this paper, we are concerned with a quasi-linear hyperbolic-parabolic system of persistence and endogenous chemotaxis modelling vasculogenesis in $\mathbb{R}$. Under some suitable structural assumption on the pressure function, we first…
We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of…
The Geometric Thin-Film equation is a mathematical model of droplet spreading in the long-wave limit, which includes a regularization of the contact-line singularity. We show that the weak formulation of the problem, given initial Radon…
An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the…