Related papers: The Free Material Design problem for stationary he…
We study a basic linear elliptic equation on a lower dimensional rectifiable set $S$ in $\mathbb{R}^N$ with the Neumann boundary data. Set $S$ is a support of a finite Borel measure $\mu$. We will use the measure theoretic tools to…
We present a space-time least squares finite element method for the heat equation. It is based on residual minimization in L2 norms in space-time of an equivalent first order system. This implies that (i) the resulting bilinear form is…
In this paper we consider a minimization problem which arises from thermal insulation. A compact connected set $K$, which represents a conductor of constant temperature, say $1$, is thermally insulated by surrounding it with a layer of…
We study the electric conductivity of hot QCD matter at various temperatures T within the off-shell parton-hadron-string dynamics transport approach for interacting partonic, hadronic or mixed systems in a finite box with periodic boundary…
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…
Current-carrying conductors inevitably experience resistive heating due to the material's finite electrical conductivity. The resulting temperature distribution within the wire has essential implications for structural integrity,…
We analyze an optimization problem of the conductivity in a composite material arising in a heat conduction energy storage problem. The model is described by the heat equation that specifies the heat exchange between two types of materials…
We show the existence and optimal regularity of the optimal temperature configuration in a problem in heat conduction with minimal temperature constraint, interior heating and exterior insulation. Regularity of the two free boundaries is…
In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…
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 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…
We extend [Bru-de Siqueira Pedra-Hertling, J. Math. Phys. 56 (2015) 051901] in order to study the linear response of free fermions on the lattice within a (independently and identically distributed) random potential to a macroscopic…
The quantum theory of conductivity of semiconductor objects, to which the quantum wells, wires and dots concern, is constructed. Average values of current and charge densities, induced by a weak electromagnetic field, are calculated. It is…
In this paper, we study the heat equation with an irregular spatially dependent thermal conductivity coefficient. We prove that it has a solution in an appropriate very weak sense. Moreover, the uniqueness result and consistency with the…
Backward parabolic equations, such as the backward heat equation, are classical examples of ill-posed problems where solutions may not exist or depend continuously on the data. In this work, we study a least squares finite element method to…
We developed a novel contactless frequency-domain approach to study thermal transport, which is particularly convenient when thermally anisotropic materials are considered. The method is based on a similar line-shaped heater geometry as…
The objective of this paper is to study the plane symmetric kinematic self-similar heat conducting fluid and charge dust solutions of the Einstein field equations. These solutions are classified according to self-similarity of the first,…
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…