Related papers: Heat equation with a general stochastic measure on…

In this paper, we consider the exponential stabilization and observation of an unstable heat equation in a general multi-dimensional domain by combining the finite-dimensional spectral truncation technique and the recently developed…

We consider heat transfer in an infinite two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a heat source. The basic equations for the particles of the lattice are stated in the form of a system…

We study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. For this aim, we establish decay estimates of the fractional heat semigroup in several uniformly local Zygumnd spaces.…

We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…

We consider the stochastic heat equation with multiplicative noise $u_t={1/2}\Delta u+ u \diamond \dot{W}$ in $\bR_{+} \times \bR^d$, where $\diamond$ denotes the Wick product, and the solution is interpreted in the mild sense. The noise…

The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees…

We analyze the nonlinear stochastic heat equation driven by heavy-tailed noise in free space and arbitrary dimension. The existence of a solution is proved even if the noise only has moments up to an order strictly smaller than its…

An analytical model of unsteady heat transfer in a one-dimensional harmonic crystal is presented. A nonlocal temperature is introduced as a generalization of the kinetic temperature. A closed equation determining unsteady thermal processes…

We consider a non-linear, one-dimensional wave equation system with finite-dimensional stochastic driving terms and with weak dissipation. A stationary process that solves the system is used to model steady-state non-equilibrium heat flow…

Stochastic heating is a well-known mechanism through which magnetized particles may be energized by low-frequency electromagnetic waves. In its simplest version, under spatially homogeneous conditions, it is known to be operative only above…

We consider the stochastic heat equation on a compact smooth Riemannian manifold without boundary satisfying \begin{equation*} \partial_tu(t,x)=\frac{1}{2}\Delta_Mu(t,x)+\sigma(t,x,u)\dot{W}(t,x),\quad (t,x)\in\mathbb{R}_+\times M,…

We prove the existence and uniqueness of a mild solution for a class of non-autonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset $D \subset \mathbb{R}^d$ and involving standard and fractional…

We consider for an anyon gas its termodynamics properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or…

The agreement between the fragments' internal and kinetic temperatures with the breakup temperature is investigated using a Statistical Multifragmentation Model which makes no a priori as- sumption on the relationship between them. We thus…

This paper deals with the solution of an inverse problem for the heat equation aimed at nondestructive evaluation of fractures. A fundamental step in any typical iterative inversion method, is the numerical solution of the underlying direct…

In this article we consider the stochastic heat equation $u_{t}-\Delta u=\dot B$ in $(0,T) \times \bR^d$, with vanishing initial conditions, driven by a Gaussian noise $\dot B$ which is fractional in time, with Hurst index $H \in (1/2,1)$,…

In this paper, we give a review of fractal calculus which is an expansion of standard calculus. Fractal calculus is applied for functions which are not differentiable or integrable on totally disconnected fractal sets such as middle-$\mu$…

We study the numerical approximation of the stochastic heat equation with a distributional reaction term. Under a condition on the Besov regularity of the reaction term, it was proven recently that a strong solution exists and is unique in…

In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coeffcient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this…

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of…