Related papers: Heat equation with singular thermal conductivity
We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, with constant restitution coefficient $\alpha\in(0,1)$, under the thermalization induced by a host medium with a fixed Maxwellian distribution and any…
Thermal measurements of heat capacity and thermal conductivity in a wide range of insulators and superconductors exhibit a ``thermal paradox": a large linear specific heat reminiscent of neutral Fermi surfaces in samples that exhibit no…
We study the dynamical thermal conductivity of the Kitaev spin model on a two-leg ladder. In contrast to conventional integrable one-dimensional spin systems, we show that heat transport is completely dissipative. This is a direct…
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…
We define a deterministic ``scattering'' model for heat conduction which is continuous in space, and which has a Boltzmann type flavor, obtained by a closure based on memory loss between collisions. We prove that this model has, for…
Analytic solutions for cylindrical thermal waves in solid medium is given based on the nonlinear hyperbolic system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law is generalized where the…
We examine the temperature dependence of thermal conductivity of one dimensional nonlinear (anharmonic) lattices with and without on-site potential. It is found from computer simulation that the heat conductivity depends on temperature via…
A new proof of a pathwise uniqueness result of Krylov and R\"{o}ckner is given. It concerns SDEs with drift having only certain integrability properties. In spite of the poor regularity of the drift, pathwise continuous dependence on…
We introduce a model whose thermal conductivity diverges in dimension 1 and 2, while it remains finite in dimension 3. We consider a system of oscillators perturbed by a stochastic dynamics conserving momentum and energy. We compute thermal…
Evaluation of effective or macroscopic coefficients of thermal conductivity under coupled heat and moisture transfer is presented. The paper first gives a detailed summary on the solution of a simple steady state heat conduction problem…
We study the heat equation with a random potential term. The potential is a one-sided stable noise, with positive jumps, which does not depend on time. To avoid singularities, we define the equation in terms of a construction similar to the…
In this paper we study removable singularities for solutions of the fractional heat equation in time varying domains. We introduce associated capacities and we study some of its metric and geometric properties.
We investigate heat propagation in rigidly rotating bodies within the theory of general relativity. Using a first-order gradient expansion, we derive a universal partial differential equation governing the temperature evolution. This…
The goal of this paper is to prove a uniqueness result for a stochastic heat equation with a randomly perturbed potential, which can be considered as a variant of Hardy's uncertainty principle for stochastic heat evolutions.
The optimal insulation of a heat conducting body by a thin film of variable thickness can be formulated as a nondifferentiable, nonlocal eigenvalue problem. The discretization and iterative solution for the reliable computation of…
We consider one-dimensional stochastic heat equation with nonlinear drift, $\displaystyle \partial_t u=\frac{1}{2}\Delta u+b(u)u+\sigma(u)\dot{W}(t,x)$, where $b:\mathbb{R}_{+}\to \mathbb{R}$ is a continuous function and…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
An accurate analysis of the conduction heat transfer in a cryogenic flask is made and some useful formulae are derived. Taking into account the temperature dependence of conductivity and tensile strength of the supporting rods for a helium…
It has recently been shown theoretically that the time-dependent heat conduction equation is form-invariant under curvilinear coordinate transformations. Thus, in analogy to transformation optics, fictitious transformed space can be mapped…
The one-dimensional problem of the nonlinear heat equation is considered. We assume that the heat flow in the origin of coordinates is the power function of time and the initial temperature is zero. Approximate solutions of the problem are…