Related papers: Determine the source term of a two-dimensional hea…
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,g) be a compact, connected riemannian manifold that is homogeneous, i.e. each pair of points p,q in M have isometric neighborhoods. This paper is a first step towards an understanding of the extent to which it is true that for each…
We consider the stochastic heat equation $$\frac{\partial Y_t(x)}{\partial t} = \frac{1}{2} \Delta_x Y_t(x) + Y_{t-}(x)^{\beta} \dot{L}^{\alpha}$$ with $t \ge 0$, $x \in \mathbb{R}$ and $L^{\alpha}$ being an $\alpha$-stable white noise…
We study heat conduction in a one-dimensional {finite}, unpinned chain of atoms perturbed by stochastic momentum exchange and coupled to Langevin heat baths at {possibly} distinct temperatures placed at the endpoints of the chain. While…
We analyze the non-Fourier dual-phase-lag heat conduction process in a three-dimensional medium heated by a moving circular or annular laser beam, which is modeled by a set of point heat sources in the cross-section. In order to solve the…
Motivated by the search for sharp bounds on turbulent heat transfer as well as the design of optimal heat exchangers, we consider incompressible flows that most efficiently cool an internally heated disc. Heat enters via a distributed…
In this paper we investigate the propagation of singularities in a nonlinear parabolic equation with strong absorption when the absorption potential is strongly degenerate following some curve in the $(x,t)$ space. As a very simplified…
We derive the dynamic boundary condition for the heat equation as a limit of boundary layer problems. We study convergence of their weak and strong solutions as the width of the layer tends to zero. We also discuss $\Gamma$-convergence of…
In this work the authors consider an inverse source problem in the following stochastic fractional diffusion equation $$\partial_t^\alpha u(x,t)+\mathcal{A} u(x,t)=f(x)h(t)+g(x) \dot{\mathbb{W}}(t).$$ The interested inverse problem is to…
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…
We study the one-dimensional one-phase Stefan problem for the heat equation with a nonlinear boundary condition. We show that all solutions fall into one of three distinct types: global-in-time solutions with exponential decay,…
We give a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is…
Surface heat flow is a key parameter for the geothermal structure, rheology, and hence the dynamics of continents. However, the coverage of heat flow measurements is still poor in many continental areas. By transforming the stable nonlinear…
The simultaneous determination of two unknown thermal coefficients for a semi-infinite material under a phase-change process with a mushy zone according to the Solomon-Wilson-Alexiades model is considered. The material is assumed to be…
Recently, Nair and Danumjaya (2023) introduced a new regularization method for the homogeneous time-fractional backward heat conduction problem (TFBHCP) in a one-dimensional space variable, for determining the initial value function. In…
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 stationary nonequilibrium states of a quasi one-dimensional system of heavy particles whose interaction is mediated by purely elastic collisions with light particles, in contact at the boundary with two heat baths with…
Recent simulation results on heat conduction in a one-dimensional chain with an asymmetric inter-particle interaction potential and no onsite potential found non-anomalous heat transport in accordance to Fourier's law. This is a surprising…
This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet…
We give a uniform bound from below on the temperature for a variant of the compressible Navier-Stokes-Fourier system, under suitable hypotheses. This system of equations forms a mathematical model of the motion of a compressible fluid…