Related papers: Inverse Conduction Problem for a Parabolic Equatio…
In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…
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…
A broad class of inverse problems deals with determining certain parameters, from measurement data, in models which are associated to certain partial differential equations. In this work we focus on the heat equation on a finite interval…
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…
A stochastic inverse heat transfer problem is formulated to infer the transient heat flux, treated as an unknown Neumann boundary condition. Therefore, an Ensemble-based Simultaneous Input and State Filtering as a Data Assimilation…
A problem of diffraction by an elongated body of revolution is studied. The incident wave falls along the axis. The wavelength is small comparatively to the dimensions of the body. The parabolic equation of the diffraction theory is used to…
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…
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…
We investigate the control problem of harmonic map heat flow by means of an external magnetic field. In contrast to the situation of a parabolic system with internal or boundary control, the magnetic field acts as the coefficients of the…
In this paper we develop numerical algorithm for solving inverse problem for the wave equation using Boundary Control method. The results of numerical experiments are represented.
This paper focuses on the numerical solution of a dual-phase-lag heat conduction equation on a space unbounded domain. First, based on the Laplace transform and the Pad\'e approximation, a high-order local artificial boundary condition is…
We study the inverse problems for the second order hyperbolic equations of general form with time-dependent coefficients assuming that the boundary data are given on a part of the boundary. The main result of this paper is the determination…
We consider the problem of determining an unaccessible part of the boundary of a conductor by mean of thermal measurements. We study a problem of corrosion where a Robin type condition is prescribed on the damaged part and we prove…
This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…
In this work, we initiate the study of the biharmonic heat equation in a spatial bounded domain subject to dynamic boundary conditions involving the bi-Laplace-Beltrami operator on the boundary. The boundary heat equation is coupled to the…
We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with…
In this paper we solve the inverse problem for the cubic mean-field Ising model. Starting from configuration data generated according to the distribution of the model we reconstruct the free parameters of the system. We test the robustness…
We consider a heat conduction problem $S$ with mixed boundary conditions in a n-dimensional domain $\Omega$ with regular boundary $\Gamma$ and a family of problems $S_{\alpha}$, where the parameter $\alpha>0$ is the heat transfer…
A simple idea of finding a domain that encloses an unknown discontinuity embedded in a body is introduced by considering an inverse boundary value problem for the heat equation. The idea gives a design of a special heat flux on the surface…
In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…