相关论文: Two-phase heat conductors with a surface of the co…

We consider a two-phase heat conductor in two dimensions consisting of a core and a shell with different constant conductivities. When the medium outside the two-phase conductor has a possibly different conductivity, we consider the Cauchy…

We consider a two-phase heat conductor in $\mathbb R^N$ with $N \geq 2$ consisting of a core and a shell with different constant conductivities. Suppose that, initially, the conductor has temperature 0 and, at all times, its boundary is…

We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one medium has temperature 0 and the other has temperature 1. Under…

We consider the Cauchy problem for the heat diffusion equation in the whole space consisting of three layers with different constant conductivities, where initially the upper and middle layers have temperature 0 and the lower layer has…

We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one has temperature 0 and the other has temperature 1. Suppose that…

We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media locally with different constant conductivities, where initially one medium has temperature 0 and the other has temperature…

In this paper, we consider a parabolic counterpart of Serrin's overdetermined problem, in which the overdetermined condition (constant flux condition) is imposed only on a discrete infinite set of time values. We show that, under suitable…

Let $\Omega$ be a compact Riemannian manifold with smooth boundary and let $u_t$ be the solution of the heat equation on $\Omega$, having constant unit initial data $u_0=1$ and Dirichlet boundary conditions ($u_t=0$ on the boundary, at all…

We study a two-phase parabolic free boundary problem motivated by the jump of conductivity in composite materials that undergo a phase transition. Each phase is governed by a heat equation with distinct thermal conductivity, and a…

A celebrated theorem of Serrin asserts that one overdetermined condition on the boundary is enough to obtain radial symmetry in the so-called one-phase overdetermined torsion problem. It is also known that imposing just one overdetermined…

Let $S$ be a smooth hypersurface properly embedded in $\mathbb R^N$ with $N \geq 3$ and consider its tubular neighborhood $\mathcal N$. We show that, if a heat flow over $\mathcal N$ with appropriate initial and boundary conditions has $S$…

The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the…

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…

Let $M$ be a Riemannian manifold and $\Omega$ a compact domain of $M$ with smooth boundary. We study the solution of the heat equation on $\Omega$ having constant unit initial conditions and Dirichlet boundary conditions. The purpose of…

We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities. The large time behavior of temperature, the solution of the problem, is studied when…

We investigate heat circulators where a phase coherent region is contacted by three leads that are either normal- or superconducting. A magnetic field, and potentially the superconducting phases, allow to control the preferential direction…

We define a `hyperconductor' to be a material whose electrical and thermal DC conductivities are infinite at zero temperature and finite at any non-zero temperature. The low-temperature behavior of a hyperconductor is controlled by a…

This is the second part of a two parts work on the analysis of heat-type equations on manifolds with fibered boundary equipped with a $\Phi$-metric. This setting generalizes the asymptotically conical (scattering) spaces and includes…

An analytic solution to a stationary heat conduction problem in 2D unbounded doubly periodic composite materials with temperature dependent conductivities of their components is given. Corresponding nonlinear boundary value problem is…

We investigate the heat flow between different terminals in an interacting coherent conductor when inelastic scattering is present. We illustrate our theory with a two-terminal quantum dot setup. Two types of heat asymmetries are…