Related papers: Nonlinear diffusion with a bounded stationary leve…
We study spherical, charged and self--similar distributions of matter in the diffusion approximation. We propose a simple, dynamic but physically meaningful solution. For such a solution we obtain a model in which the distribution becomes…
The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a…
We study the boundedness and convergence to equilibrium of weak solutions to reaction-diffusion systems with nonlinear diffusion. The nonlinear diffusion is of porous medium type and the nonlinear reaction terms are assumed to grow…
The nonlinear Schroedinger equation in the presence of disorder is considered. The dynamics of an initially localized wave packet is studied. A subdiffusive spreading of the wave packet is explained in the framework of a continuous time…
In this article we develop an effective theory of pulse propagation in a nonlinear and disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel…
We construct solutions of nonlinear reaction-diffusion equations with nonlinear boundary conditions in spaces where the problem is supercritical and show the nonlinear balance required between the nonlinear terms in order to obtain a…
We consider a dense neutrino gas in the "fast-flavor limit" (vanishing neutrino masses). For the first time, we identify exact solutions of the nonlinear wave equation in the form of solitons. They can propagate with both sub- or…
We suppose that a rigid spherical particle is put into a binary fluid mixture with the critical composition in the homogeneous phase near the demixing critical point. A short-range interaction is assumed between each component and the…
In this article we study the shape of a compact surface of constant mean curvature of Euclidean space whose boundary is contained in a round sphere. We consider the case that the boundary is prescribed or that the surface meets the sphere…
We consider a chemotaxis-fluid system involving nonlinear cell diffusion of porous medium type, signal consumption by cells, and rather general, possibly matrix-valued, chemotactic sensitivities. It is shown that if the corresponding…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
Consider a pair of smooth, possibly noncompact, properly immersed hypersurfaces moving by mean curvature flow, or, more generally, a pair of weak set flows. We prove that if the ambient space is Euclidean space and if the distance between…
Let ($M$, $\Omega$) be a smooth symplectic manifold and $f:M\rightarrow M$ be a symplectic diffeomorphism of class $C^l$ ($l\geq 3$). Let $N$ be a compact submanifold of $M$ which is boundaryless and normally hyperbolic for $f$. We suppose…
A version of fractional diffusion on bounded domains, subject to 'homogeneous Dirichlet boundary conditions' is derived from a kinetic transport model with homogeneous inflow boundary conditions. For nonconvex domains, the result differs…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
We consider stochastic diffusion processes absorbed at the boundary of a domain. It is shown that there exist initial distributions which ensure a given decreasing of density of the absorbed process.
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…
We study the fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional…
Using graph-theoretic methods we give a new proof that for all sufficiently large $n$, there exist sphere packings in $\R^n$ of density at least $cn2^{-n}$, exceeding the classical Minkowski bound by a factor linear in $n$. This matches up…
Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates…