Related papers: Third Boundary-Value Problem of the Heat Conductio…
In the literature, one can find numerous modifications of Fourier's law from which the first one is called Maxwell-Cattaneo-Vernotte heat equation. Although this model has been known for decades and successfully used to model…
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…
This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions…
We consider initial-boundary value problems (IBVPs) on a finite interval for the system of the energy balance equation and Guyer-Krumhansl constitutive equation. Boundary conditions comprise various models of behavior of a physical system…
Consider the steady Boltzmann equation with slab symmetry for a monatomic, hard sphere gas in a half space. At the boundary of the half space, it is assumed that the gas is in contact with its condensed phase. The present paper discusses…
In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary…
The influence of fixed temperature and fixed heat flux thermal boundary conditions on rapidly rotating convection in the plane layer geometry is investigated for the case of stress-free mechanical boundary conditions. It is shown that…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…
In the study of the heat transfer in the Boltzmann theory, the basic problem is to construct solutions to the steady problem for the Boltzmann equation in a general bounded domain with diffuse reflection boundary conditions corresponding to…
A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition at the face $x=0$ is studied with the aim of finding explicit…
We consider a heat conduction problem $S$ with mixed boundary conditions in a n-dimensional domain $\Omega$ with regular boundary $\Gamma$ and a family of problems $S_{\alpha}$, where the parameter $\alpha>0$ is the heat transfer…
The effects of MHD boundary layer flow of non-linear thermal radiation with convective heat transfer and non-uniform heat source/sink in presence of thermophortic velocity and chemical reaction investigated in this study. Suitable…
We consider the identification of nonlinear heat conduction laws in stationary and instationary heat transfer problems. Only a single additional measurement of the temperature on a curve on the boundary is required to determine the unknown…
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…
In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary…
It has been observed in many numerical simulations, experiments and from various theoretical treatments that heat transport in one-dimensional systems of interacting particles cannot be described by the phenomenological Fourier's law. The…
Motion in the atmosphere or mantle convection are two among phenomena of natural convection induced by internal heat sources. They bifurcate from the conduction state as a result of its loss of stability. In spite of their importance, due…
Consider neutron transport equations in 3D convex domains with in-flow boundary. We mainly study the asymptotic limits as the Knudsen number $\epsilon\rightarrow 0^+$. Using Hilbert expansion, we rigorously justify that the solution of…
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…
We study the heat equation on a half-space or on an exterior domain with a linear dynamical boundary condition. Our main aim is to establish the rate of convergence to solutions of the Laplace equation with the same dynamical boundary…