Related papers: Some remarks on optimal insulation with Robin boun…
We consider the homogenization of an optimal control problem in which the control is placed on a part of the boundary and the spatial domain contains a thin layer of "small particles", very close to the controlling boundary, and a Robin…
We consider convection in an internally heated layer of fluid that is bounded below by a perfect insulator and above by a poor conductor. The poorly conducting boundary is modelled by a fixed heat flux. Using solely analytical methods, we…
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 give a counterexample to the long standing conjecture that the ball maximises the first eigenvalue of the Robin eigenvalue problem with negative parameter among domains of the same volume. Furthermore, we show that the conjecture holds…
We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin…
We study a Robin boundary problem for degenerate parabolic equation. We suggest a notion of entropy solution and propose a result of existence and uniqueness. Numerical simulations illustrate some aspects of solution behaviour.…
Convection in a spherical shell is widely used to model fluid layers of planets and stars. The choice of thermal boundary conditions in such models is not always straightforward. To understand the implications of this choice, we report on…
We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain $D\subset\R^d$ and its weak formulation is in the form of a…
In this paper we study the distribution of the temperature within a body where the heat is transported only by radiation. Specifically, we consider the situation where both emission-absorption and scattering processes take place. We study…
By tailoring the geometry of the upper boundary in turbulent Rayleigh-B\'enard convection we manipulate the boundary layer -- interior flow interaction, and examine the heat transport using the Lattice Boltzmann method. For fixed amplitude…
Let $\Omega \subset \mathbb{R}^N$, $N\ge 2$, be an open, connected, bounded set with $C^2$ boundary. In this paper we consider the torsion problem with Robin boundary conditions and we study the symmetry of the solutions when suitable extra…
We consider two optimization problems in thermal insulation: in both cases the goal is to find a thin layer around the boundary of the thermal body which gives the best insulation. The total mass of the insulating material is prescribed..…
An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, of negligible diameter, made up of two consecutive sections of different, isotropic and homogeneous materials. At the…
In this paper, we study an insulation problem that seeks the optimal distribution of a fixed amount $m>0$ of insulating material coating an insulated boundary $\Gamma_I\subseteq \partial\Omega$ of a thermally conducting body…
The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented…
Given the eigenvalue problem for the Laplacian with Robin boundary conditions, (with $\beta\in\R\setminus\{0\}$ the Robin parameter), we consider a shape minimization problem for a function of the first eigenvalues if $\beta>0$ and a shape…
We obtained a new representation of a solution of the heat conduction equation with boundary condition of the third kind for a layer. The result is presented as a superposition of fundamental solutions for an unbounded system with variable…
An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, made up of two consecutive sections of different, isotropic and homogeneous materials, perfectly assembly, where one of…
We present some new bounds for the first Robin eigenvalue with a negative boundary parameter. These include the constant volume problem, where the bounds are based on the shrinking coordinate method, and a proof that in the fixed perimeter…
We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal…