Related papers: Effective Boundary Conditions Arising from the Hea…
We discuss the initial boundary value problem for a heat equation in a domain surrounded by a layer. The main features of this problem are twofold: on one hand, the layer is thin compared to the scale of the domain, and on the other hand,…
We consider the Fisher-KPP equation on a three-dimensional domain surrounded by a thin layer whose diffusion rates are drastically different from that in the bulk. The bulk is isotropic, while the layer is considered to be anisotropic and…
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…
Here we build some effective boundary conditions to be used in numerical calculations in order to avoid the thin meshing usually required in problems involving Hartmann layers near a locally plane wall. Wall model are provided for both…
We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic domain. The time dependence is handled, based on Lubich's…
In this paper, we study optimization of the first eigenvalue of the heat equation with spatially nonuniform conductivity on a bounded domain under several constraints for the conductivity. We consider this problem in various boundary…
We consider the initial boundary problem of 2D non-homogeneous incompressible heat conducting Navier-Stokes equations with vacuum, where the viscosity and heat conductivity depend on temperature in a power law of Chapman-Enskog. We derive…
We consider an optimal insulation problem of a given domain in $\mathbb R^N$. We study a model of heat trasfer determined by convection; this corresponds, before insulation, to a Robin boundary value problem. We deal with a prototype which…
We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open 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…
In a domain of the Euclidean space, we estimate from below the distance to the boundary of global maximum points of solutions of elliptic and parabolic equations with homogeneous Dirichlet boundary values. As reference cases, we first…
We consider the initial boundary value problem of non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random perturbation. The space boundary is Lipschitz and we impose non-zero…
We study the well-posedness of the compressible boundary layer equations with data being analytic in the tangential variable of the boundary. The compressible boundary layer equations, a nonlinear coupled system of degenerate parabolic…
A semi-explicit formula of solution to the boundary layer system for thermal layer derived from the compressible Navier-Stokes equations with the non-slip boundary condition when the viscosity coefficients vanish is given, in particular in…
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…
Three inverse boundary value problems for the heat equations in one space dimension are considered. Those three problems are: extracting an unknown interface in a heat conductive material, an unknown boundary in a layered material or a…
This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak…
The optimal insulation of a heat conducting body by a thin film of variable thickness can be formulated as a nondifferentiable, nonlocal eigenvalue problem. The discretization and iterative solution for the reliable computation of…
This paper studies a prototype of inverse initial boundary value problems whose governing equation is the heat equation in three dimensions. An unknown discontinuity embedded in a three-dimensional heat conductive body is considered. A {\it…
We study the thermal insulation of a bounded body $\Omega\subset\mathbb{R}^n$, under a prescribed heat source $f>0$, via a bulk layer of insulating material. We consider a model of heat transfer between the insulated body and the…