Related papers: A uniqueness theorem for the martingale problem de…

This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation…

We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…

The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of…

In this paper, we provide a mathematical framework in studying the wave propagation with the annihilation phenomenon in excitable media. We deal with the existence and uniqueness of solutions to a one-dimensional free boundary problem…

We construct a scattering matrix with operator valued entries describing solutions to the 1+1 wave equation where permittivities has memory and depends on time and space. It is the analogue of the scattering matrix for spatially localised…

I derive a temporally propagated uni-directional optical pulse equation valid in the few cycle limit. Temporal propagation is advantageous because it naturally preserves causality, unlike the competing spatially propagated models. The exact…

We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with…

We consider diffusion of independent molecules in an insulated Euclidean domain with unknown diffusivity parameter. At a random time and position, the molecules may bind and stop diffusing in dependence of a given `binding potential'. The…

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…

We study the martingale problem associated with the operator $L u = \partial_s u + 1/2 \sum_{i,j=1}^{d_0} a^{ij} \partial_{ij} u + \sum_{i,j=1}^d B^{ij} x^j \partial_i u$, where $d_0 \leq d$. We show that the martingale problem is…

Using a microscopic phase-space model of the membrane system, the boundary condition at a membrane is derived. According to the condition, the substance flow across the membrane is proportional to the difference of the substance…

We consider a quasilinear KdV equation that admits compactly supported traveling wave solutions (compactons). This model is one of the most straightforward instances of degenerate dispersion, a phenomenon that appears in a variety of…

An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…

Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…

We study the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g., bedrock).…

The aim of this paper is first to review the derivation of a model describing the propagation of an optical wave in a photorefractive medium and to present various mathematical results on this model: Cauchy problem, solitary waves.

We prove convergence of symmetric diffusions on Wiener spaces by using stopping times arguments and capacity techniques. The drifts of the diffusions can be singular, we require the densities of the processes to be neither bounded from…

The existence of travelling waves for a model of concentration waves of bacteria is investigated. The model consists in a kinetic equation for the biased motion of cells following a run-and-tumble process, coupled with two…

Superluminal propagation is an intrinsic problem in the diffusion equation and has not been effectively addressed for a long time. In this work, a rigorous solution to this issue is obtained under the assumption that particles undergo a…

We present an optical picture of linear-optics superradiance, based on a single scattering event embedded in a dispersive effective medium composed by the other atoms. This linear-dispersion theory is valid at low density and in the…