Related papers: Quantitative unique continuation and observability…
We establish a unique continuation property for stochastic heat equations evolving in a bounded domain $G$. Our result shows that the value of the solution can be determined uniquely by means of its value on an arbitrary open subdomain of…
We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular we consider a KdV-BBM type equation. Explicit and IMEX Runge-Kutta type methods are used for time…
We investigate the fractional diffusion approximation of a kinetic equation set in a bounded interval with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
We find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with time-independent coefficients and apply them to obtain observability inequalities for its solutions over measurable sets.
In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by L\'{e}vy processes, which are sometimes called super-diffusion equations. In this article, we…
We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be…
Longstanding problems regarding the causality of the diffusion equation are resolved through a class of exact solutions. A universal differential solution for diffusive processes is derived that is causal and exact at any analytic point in…
We study analytically and numerically a bistable reaction-diffusion equation on an arbitrary finite network. We prove that stable fixed points (multi-fronts) exist for any configuration as long as the diffusion is small. We also study fold…
We study the quantitative unique continuation on the boundary for solutions of elliptic equations with Neumann boundary conditions for bounded potentials and boundary potentials on compact manifolds with boundary. The boundary doubling…
We approximate the uniform measure on an equilateral triangle by a measure supported on $n$ points. We find the optimal sets of points ($n$-means) and corresponding approximation (quantization) error for $n\leq4$, give numerical…
A quantum thermodynamic system can conserve non-commuting observables, but the consequences of this phenomenon on relaxation are still not fully understood. We investigate this problem by leveraging an observable-dependent approach to…
We propose a simple quantum mechanical model describing the time dependent diffusion current between two fermion reservoirs that were initially disconnected and characterized by different densities or chemical potentials. The exact,…
We study a fractional diffusion problem in the divergence form in one space dimension. We define a notion of the viscosity solution. We prove existence of viscosity solutions to the fractional diffusion problem with the Dirichlet boundary…
We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially…
We shall study special regularity properties of solutions to some nonlinear dispersive models. The goal is to show how regularity on the initial data is transferred to the solutions. This will depend on the spaces where regularity is…
We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…
We consider stochastic non-linear diffusion equations with a highly singular diffusivity term and multiplicative gradient-type noise. We study existence and uniqueness of non-negative variational solutions in terms of stochastic variational…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small…