Related papers: Probabilistic representations of solutions to the …
We obtain explicit expressions for one unknown thermal coefficient (among the conductivity, mass density, specific heat and latent heat of fusion) of a semi-infinite material through the one-phase fractional Lam\'e-Clapeyron-Stefan problem…
Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic…
In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators and is developed in the setting of graded Lie groups. The…
We apply the postquasistatic approximation to study the evolution of spherically symmetric fluid distributions undergoing dissipation in the form of radial heat flow. For a model which corresponds to an incompressible fluid departing from…
In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given…
We consider the stochastic heat equation $\partial_{s}u =\frac{1}{2}\Delta u +(\beta V(s,y)-\lambda)u$, with a smooth space-time stationary Gaussian random field $V(s,y)$, in dimensions $d\geq 3$, with an initial condition…
A fractional Stefan problem with a boundary convective condition is solved, where the fractional derivative of order $ \alpha \in (0,1) $ is taken in the Caputo sense. Then an equivalence with other two fractional Stefan problems (the first…
One considers the motion of a test particle in an homogeneous fluid in equilibrium at temperature $T$, undergoing dissipative collisions with the fluid particles. It is shown that the corresponding linear Boltzmann equation still posseses a…
We provide a detailed (and fully rigorous) derivation of several fundamental properties of bounded weak solutions to initial-value problems for general conservative 2nd-order parabolic equations with p-Laplacian diffusion and (arbitrary)…
In this paper, we study the partial convexity of smooth solutions to the heat equation on a compact or complete non-compact Riemannian manifold M or Kahler-Ricci flow. We show that under a natural assumption, a new partial convexity…
We consider a thermal particle which is diffusing in velocity-space and in a weakly confining potential characterized by the inverse hyperbolic sine function of the particle velocity $v$ and the control parameter $v_c$. The stationary state…
We give an explicit representation of the fundamental solution to the heat equation on a half-space of ${\mathbb R}^N$ with the homogeneous dynamical boundary condition, and obtain upper and lower estimates of the fundamental solution.…
This article studies the aggregation diffusion equation \[ \partial_t\rho = \Delta^\frac{\alpha}{2} \rho + \lambda\,\mathrm{div}((K*\rho)\rho), \] where $\Delta^\frac{\alpha}{2}$ denotes the fractional Laplacian and $K =…
Consider the following stochastic heat equation, \begin{align*} \frac{\partial u_t(x)}{\partial t}=-\nu(-\Delta)^{\alpha/2} u_t(x)+\sigma(u_t(x))\dot{F}(t,\,x), \quad t>0, \; x \in R^d. \end{align*} Here $-\nu(-\Delta)^{\alpha/2}$ is the…
In this work we construct the heat kernel of the 1/2-order Laplacian perturbed by the first-order gradient term in H\"older space and the zero-order potential term in generalized Kato's class, and obtain sharp two-sided estimates as well as…
Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the ``degree of nonequilibrium'', and has a very…
In this article we prove the existence of Bernstein processes which we associate in a natural way with a class of linear parabolic initial-and final boundary value problems defined in bounded convex subsets of Euclidean space of arbitrary…
Heat conduction is quite common in natural, industrial, and military applications. In this work, the updated Lagrangian particle hydrodynamics (ULPH) theory, is utilized and applied to solve heat conduction problems. Since heat conduction…
This article investigates spatiotemporally discrete or continuous stochastic descriptions, where we focus on differences in heat naturally defined between the particle level and the density field. Both the descriptions are found to…
We obtain the viscosity solution of G-heat equation with the initial condition $\phi(x)=x^{n}$ for each integer $n\geq1$ using the method of G-Brownian motion.