Consider the solution Z(t,x) of one-dimensional stochastic heat equation, with a multiplicative spacetime white noise, and delta initial data Z(0,x)=?(x). For any real p>0, we obtained detailed estimates pth moment et/12Z(2t,0), as t??, from these establish one-point upper-tail large deviation principle Kardar–Parisi–Zhang equation. The deviations have speed t rate function ?+(y)=43y3/2. Our re...

In this article, we study a d-dimensional stochastic nonlinear heat equation (SNLH) with quadratic nonlinearity, forced by fractional space-time white noise: ∂ t u − ∆u = ρ 2 +Ḃ , ∈ [0, T ] x R d 0 φ. Two types of regimes are exhibited, depending on the ranges Hurst index H (H ..., d) (0, 1) d+1. particular, show that local well-posedness resulting from Da Prato-Debussche trick, is easily obtai...

Abstract Heat transfer in skin tissue is an area of interest for medical sciences. In this paper we intend to study fractional bioheat equation for heat transfer in skin tissue with constant and sinusoidal heat flux condition on skin surface. Numerical solutions are obtained by implicit finite difference method. We study the effect of anomalous diffusion in skin tissue and compare it with norma...

This paper presents the results of modelling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in a solid material (beam) can be described by an integer order partial differential equation. However, in heterogeneous media, it can be described by a sub- or hyperdiffusion equation whic...

We study here a heat-type differential equation of order n greater than two, in the case where the time-derivative is supposed to be fractional. The corresponding solution can be described as the transition function of a pseudoprocess Ψn (coinciding with the one governed by the standard, non-fractional, equation) with a time argument Tα which is itself random. The distribution of Tα is presente...