Related papers: Stability of densities for perturbed degenerate Di…
This work focuses on stability of regime-switching diffusions consisting of continuous and discrete components, in which the discrete component switches in a countably infinite set and its switching rates at current time depend on the…
Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…
We analyze nonlinear degenerate coupled PDE-PDE and PDE-ODE systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular…
The phenomenon of random intensity patterns, for waves propagating in the presence of disorder, is well known in optics and in mesoscopic physics. We study this phenomenon for cold atomic gases expanding, by a diffusion process, in a weak…
We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…
In this paper we prove strong well-posedness for a system of stochastic differential equations driven by a degenerate diffusion satisfying a weak-type H\"ormander condition, assuming H\"older regularity assumptions on the drift coefficient.…
How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder…
In this paper we study the sensitivity of nonlinear stochastic differential equations of McKean-Vlasov type generated by stable-like processes. By using the method of stochastic characteristics, we transfer these equations to the…
The stimulated Raman scattering instability in a fully degenerate electron plasma is studied applying relativistic hydrodynamic and Maxwell equations. We demonstrated that the instability develops for weakly as well as strongly relativistic…
Presented here is a study of well-posedness and asymptotic stability of a "degenerately damped" PDE modeling a vibrating elastic string. The coefficient of the damping may vanish at small amplitudes thus weakening the effect of the…
We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…
This brief paper develops a probability density that models processes for which the physical mechanism is unknown. It has desirable properties which are not realized by densities derived from Gaussian process or other classic methods. In…
In this work we study a degenerate pseudo-parabolic system with cross diffusion describing the evolution of the densities of an unsaturated two-phase flow mixture with dynamic capillary pressure in porous medium with saturation-dependent…
We first consider an exactly solvable classical field model to understand the coherence properties and the density fluctuations of a one-dimensional (1D) weakly interacting degenerate Bose gas with repulsive interactions at temperatures…
This paper addresses the stability of a class of parabolic equations in non-cylindrical domains. We investigate the $L^\infty$-stability of systems for both nondegenerate and degenerate cases. Unlike in cylindrical domains, solutions to…
Fluid diffusion in unsaturated porous media manifests strong hysteresis effects due to surface tension on the liquid-gas interface. We describe hysteresis in the pressure-saturation relation by means of the Preisach operator, which makes…
We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…
We investigate the influence of quantum fluctuations upon dipolar Bose gases by means of the Bogoliubov-de Gennes theory. Thereby, we make use of the local density approximation to evaluate the dipolar exchange interaction between the…
In this work we derive the evolution equation for the density contrast considering open system cosmology, where the influence of adiabatic particle production process on the dynamic of a homogeneous and isotropic is investigated within a…
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic…