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We consider a semi-infinite one-dimensional phase-change material with two unknown constant thermal coefficients among the latent heat per unit mass, the specific heat, the mass density and the thermal conductivity. Aiming at the…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
The arrow of time problem remains one of the most intriguing questions of modern physics. We investigate one particular example of this problem: the irreversibility of heat transfer through an interface between two materials. This special…
We consider an inverse problem of identifying the unknown cavities in a heat conductor. Using the Neumann-to-Dirichlet map as an input data, we develop a linear sampling type method for the heat equation. A new feature is that there is a…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
We study the initial boundary value problem for a heat equation in a domain containing a thin layer. The thermal conductivity of the layer is drastically different from that of the bulk of the domain; moreover, the layer is anisotropic and…
We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as…
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…
We investigate the incompressible and compressible heat conducting boundary layer with applying the two-dimensional self-similar Ansatz. Analytic solutions can be found for the incompressible case which can be expressed with special…
We study inverse boundary problems for a one dimensional linear integro-differential equation of the Gurtin--Pipkin type with the Dirichlet-to-Neumann map as the inverse data. Under natural conditions on the kernel of the integral operator,…
This work deals with an inverse boundary value problem arising from the equation of heat conduction. We reconstruct small perturbations of the (isotropic) heat conductivity distribution from partial (on accessible part of the boundary)…
Understanding heat transport in one-dimensional systems remains a major challenge in theoretical physics, both from the quantum as well as from the classical point of view. In fact, steady states of one-dimensional systems are commonly…
We consider two hydrodynamic model problems (one incompressible and one compressible) with three dimensional fluid flow on the torus and temperature-dependent viscosity and conductivity. The ambient heat for the fluid is transported by the…
We study an initial-boundary-value problem for time-dependent flows of heat-conducting viscous incompressible fluids in a system of three-dimensional pipes on a time interval $(0,T)$. Here we are motivated by the bounded domain approach…
The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…
We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time…
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…
In the present Letter we present an analytical and numerical solution of the self-consistent mode-coupling equations for the problem of heat conductivity in one-dimensional systems. Such a solution leads us to propose a different scenario…
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…
In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point…