Related papers: Backward uniqueness for the heat equation in cones
In this work we investigate the inverse problem of recovering one point source in the heat equation from sparse boundary measurement, i.e., the flux data at several points on the boundary. We prove the unique recovery of the location and…
We investigate uniqueness in the inverse problem of reconstructing simultaneously a spacewise conductivity function and a heat source in the parabolic heat equation from the usual conditions of the direct problem and additional information…
Let $M$ be a Riemannian manifold and $\Omega$ a smooth domain of $M$. We study the following heat diffusion problem: assume that the initial temperature is equal to $1$, uniformly on $\Omega$, and is $0$ on its complement. Heat will then…
The heat equation with inverse square potential on both half-lines of $\mathbb{R}$ is discussed in the presence of \emph{bridging} boundary conditions at the origin. The problem is the lowest energy (zero-momentum) mode of the transmission…
This paper considerers the problem of computing the value of a solution of the heat equation at a given point inside a bounded domain after the initial time. It is assumed that the initial value of the solution inside the domain (possibly…
In this paper, we regularize the nonlinear inverse time heat problem in the unbounded region by Fourier method. Some new convergence rates are obtained. Meanwhile, some quite sharp error estimates between the approximate solution and exact…
This paper considers the initial-boundary value problem for the heat equation with a dynamic type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon…
In this article, we study certain type of boundary behaviour of positive solutions of the heat equation on the upper half-space of $\R^{n+1}$. We prove that the existence of the parabolic limit of a positive solution of the heat equation at…
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…
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…
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…
There recently has been some interest in the space of functions on an interval satisfying the heat equation for positive time in the interior of this interval. Such functions were characterised as being analytic on a square with the…
(a). Using time analyticity result, we address a basic question for a nonhomogeneous backward heat equation (exact control problem) in the setting of smooth domains and compact manifolds, namely: when is essentially time independent control…
In this paper we establish an observability inequality for the heat equation with bounded potentials on the whole space. Roughly speaking, such a kind of inequality says that the total energy of solutions can be controlled by the energy…
This article is devoted to the analysis of control properties for a heat equation with singular potential $\mu/\delta^2$, defined on a bounded $C^2$ domain $\Omega\subset\mathbb{R}^N$, where $\delta$ is the distance to the boundary…
In this article, we provide a description of the reachable space for the heat equation with various lower order terms, set in the euclidean ball of $\mathbb{R}^d$ centered at $0$ and of radius one and controlled from the whole external…
The interface temperature of two rods with equal cross section joined at one end and with different initial temperatures, initially always acquires the value characteristic for two semi-infinite rods. This value, which is shown to be a…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
We obtain (i) lower and upper bounds for the heat content of an open set in $\mathbb{R}^m$ with $R$-smooth boundary and finite Lebesgue measure, (ii) a necessary and sufficient geometric condition for finiteness of the heat content in…
The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting…