Related papers: Heat flow within convex sets

A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which…

In this paper, we consider the heat flow for p-pseudoharmonic maps from a closed Sasakian manifold M into a compact Riemannian manifold N. We prove global existence and asymptotic convergence of the solution for the p-pseudoharmonic map…

We consider the heat equation with Dirichlet boundary conditions on the tubular neighborhood of a closed Riemannian submanifold. We show that, as the tube diameter tends to zero, a suitably rescaled and renormalized semigroup converges to a…

We reinvestigate nonexistence and existence of global positive solutions to heat equation with a potential term on Riemannian manifolds. Especially, we give a very natural sharp condition only in terms of the volume of geodesic ball to…

An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…

In this paper, we investigate $V$-harmonic heat flows from complete Riemannian manifolds with nonnegative Bakry-Emery Ricci curvature to complete Riemannian manifolds with sectional curvature bounded above. We give a gradient estimate of…

We prove a bound on the heat trace of the Neumann Laplacian on a convex domain that captures the first two terms in its small-time expansion, but is valid for all times and depends on the underlying domain only through very simple geometric…

In this work, we study the decay of mass for solutions to the heat equation in exterior domains, i.e., domains which are the complement of a compact set in $\mathbb{R}^N$. Different homogeneous boundary conditions are considered, including…

Let $F:\Sigma^n \times [0,T)\to \R^{n+m}$ be a family of compact immersed submanifolds moving by their mean curvature vectors. We show the Gauss maps $\gamma:(\Sigma^n, g_t)\to G(n, m)$ form a harmonic heat flow with respect to the…

In this article, we demonstrate the phenomenon of thermal transpiration in a bounded convex domain. We employ the stationary Boltzmann equation with a cutoff potential. For boundary condition, we partition the boundary into diffuse…

A model of two-component relativistic fluid is considered, and the thermal nature of coupling between the fluid constituents is outlined. This thermal coupling is responsible for non-ideality of the fluid composite where the components are…

We prove a Li-Yau gradient estimate for positive solutions to the heat equation, with Neumann boundary conditions, on a compact Riemannian submanifold with boundary ${\bf M}^n\subseteq {\bf N}^n$, satisfying the integral Ricci curvature…

We investigate uniqueness of solution to the heat equation with a density $\rho$ on complete, non-compact weighted Riemannian manifolds of infinite volume. Our main goal is to identify sufficient conditions under which the solution $u$…

We prove that among all doubly connected domains of R^n (n>=2) bounded by two spheres of given radii, the Dirichlet heat content at any fixed time achieves its minimum when the spheres are concentric. This is shown to be a special case of a…

A mathematical model of the heat process in one-dimensional domain governed by a cylindrical heat equation with a heat source on the axis $z=0$ and nonlinear thermal coefficients is considered. The developed model is particularly applicable…

The flexible profile approach proposed earlier to create CTM (compact or reduced order thermal models) is extended to cover the area of conjugate heat transfer. The flexible profile approach is a methodology that allows building a highly…

This paper provides sharp Dirichlet heat kernel estimates in inner uniform domains, including bounded inner uniform domains, in the context of certain (possibly non-symmetric) bilinear forms resembling Dirichlet forms. For instance, the…

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 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…

Let $\Omega$ be a compact Riemannian manifold with smooth boundary and let $u_t$ be the solution of the heat equation on $\Omega$, having constant unit initial data $u_0=1$ and Dirichlet boundary conditions ($u_t=0$ on the boundary, at all…