Related papers: Some remarks on optimal insulation with Robin boun…
We study a free boundary optimization problem in heat conduction, ruled by the infinity-Laplace operator, with lower temperature bound and a volume constraint. We obtain existence and regularity results and derive geometric properties for…
We consider the dunking problem: a solid body at uniform temperature $T_\text{i}$ is placed in a environment characterized by farfield temperature $T_\infty$ and time-independent spatially uniform heat transfer coefficient; we permit…
We investigate the realization of a myriad of general local and nonlocal inhomogeneous elliptic and parabolic boundary value problems over classes of irregular regions. We present a unified approach in which either local or nonlocal…
In the framework of the optimal wave energy absorption, we solve theoretically and numerically a parametric shape optimization problem to find the optimal distribution of absorbing material in the reflexive one defined by a characteristic…
This work concerns the numerical analysis of the linear elasticity problem with a Robin boundary condition on a smooth domain. A finite element discretization is presented using high-order curved meshes in order to accurately discretize the…
We report the results of high resolution direct numerical simulations of two-dimensional Rayleigh-B\'enard convection for Rayleigh numbers up to $\Ra=10^{10}$ in order to study the influence of temperature boundary conditions on turbulent…
In this paper, we investigate an optimal design problem motivated by some issues arising in population dynamics. In a nutshell, we aim at determining the optimal shape of a region occupied by resources for maximizing the survival ability of…
We introduce Robin boundary conditions for biharmonic operators, which are a model for elastically supported plates and are closely related to the study of spaces of traces of Sobolev functions. We study the dependence of the operator, its…
This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through porous building materials. Traditionally, by using the finite-difference approach, the…
We study a nonlinear generalization of a free boundary problem that arises in the context of thermal insulation. We consider two open sets $\Omega\subseteq A$, and we search for an optimal $A$ in order to minimize a non-linear energy…
We prove new bounds on the heat flux out of the bottom boundary, $\mathcal{F}_B$, for a fluid at infinite Prandtl number, heated internally between isothermal parallel plates under two kinematic boundary conditions. In uniform internally…
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…
In this paper, an inverse initial-boundary value problem for the heat equation in three dimensions is studied. Assume that a three-dimensional heat conductive body contains several cavities of strictly convex. In the outside boundary of…
We study the asymptotic behavior of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions imposing Robin boundary conditions. Assuming the existence of…
We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a…
We consider a boundary value problem (BVP) modelling one-dimensional heat-conduction with radiation, which is derived from the Stefan-Boltzmann law. The problem strongly depends on the parameters, making difficult to estimate the solution.…
In this paper, a one-phase Stefan-type problem for a semi-infinite material which has as its main feature a variable latent heat that depends on the power of the position and the velocity of the moving boundary is studied. Exact solutions…
The diffusion system with time-fractional order derivative is of great importance mathematically due to the nonlocal property of the fractional order derivative, which can be applied to model the physical phenomena with memory effects. We…
This paper is concerned with the problem of enhancing convection-cooling via active control of the incompressible velocity field, described by a stationary diffusion-convection model. This essentially leads to a bilinear optimal control…
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)…