Related papers: Heat equation with a general stochastic measure on…
In this article, we give some existence and smoothness results for the law of the solution to a stochastic heat equation driven by a finite dimensional fractional Brownian motion with Hurst parameter $H>1/2$. Our results rely on recent…
In this paper, we prove pathwise uniqueness for stochastic differential equations in infinite dimension. Under our assumptions, we are able to consider the stochastic heat equation up to dimension $3$, the stochastic damped wave equation in…
A microscopic nuclear equation of state compatible with all current astrophysical constraints constructed within the Brueckner-Hartree-Fock formalism is presented and extended in a consistent way to finite temperature. The effects of finite…
We consider the stochastic heat equation on $\mathbb R^d$ with multiplicative space-time white noise noise smoothed in space. For $d\geq 3$ and small noise intensity, the solution is known to converge to a strictly positive random variable…
We prove existence, uniqueness and regularity of solutions of nonlocal heat equations associated to anisotropic stable diffusion operators. The main features are that the right-hand side has very few regularity and that the spectral measure…
We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.
In this paper, we study a nonlinear one spatial dimensional stochastic heat equations driven by Gaussian noise: $\frac{\partial u }{\partial t}=\frac{\partial^2 u }{\partial x^2}+\sigma(u )\dot{W} $, where $\dot{W} $ is white in time and…
In this paper, we study quantitative spatial analytic bounds and unique continuation inequalities of solutions for fractional heat equations with an analytic lower order term on the whole space. At first, we show that the solution has a…
Let u = {u(t, x), t $\in$ [0, T ], x $\in$ R d } be the solution to the linear stochastic heat equation driven by a fractional noise in time with correlated spatial structure. We study various path properties of the process u with respect…
In this article, we derive the stochastic master equations corresponding to the statistical model of a heat bath. These stochastic differential equations are obtained as continuous time limits of discrete models of quantum repeated…
A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space-time white noise is presented. The standard finite difference approximation is used in space and a stochastic exponential method…
In this paper, a partial integro-differential equation modeling of coagulation and multiple fragmentation events is studied. Our purpose is to investigate the global existence of gelling weak solutions to the continuous coagulation and…
In this article we study a mathematical model of the heat transfer in semi infinite material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component is…
We study the linear heat equation on a halfspace with a linear dynamical boundary condition. We are interested in an appropriate choice of the function space of initial functions such that the problem possesses a solution. It was known…
A one-dimensional stochastic wave equation driven by a general stochastic measure is studied in this paper. The Fourier series expansion of stochastic measures is considered. It is proved that changing the integrator by the corresponding…
A steady state of a granular gas with homogeneous granular temperature, no mass flow, and nonzero heat flux is studied. The state is created by applying an external position--dependent force or by enclosing the grains inside a curved…
Stochastic Thermodynamics (ST) extends the notions of classical thermodynamics to trajectories taken from a nonequilibrium ensemble. This extension yields a simple approach to fluctuation relations in small systems. Multiple time- and…
In this paper, we study the Moderate Deviation Principle for a perturbed stochastic heat equation in the whole space $\rr^d, d\ge1$. This equation is driven by a Gaussian noise, white in time and correlated in space, and the differential…
In this work, we investigate the one-dimensional heat equation within the framework of Stieltjes calculus. We first consider the equation associated with two fixed derivators and develop a constructive approach to establish the existence of…
This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W is a mean zero Gaussian noise and the differential element uW is interpreted both in the sense of Skorohod and Stratonovich. The existence…