English
Related papers

Related papers: Inverse Conduction Problem for a Parabolic Equatio…

200 papers

This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…

Numerical Analysis · Mathematics 2022-08-25 Angel A. Ciarbonetti , Sergio Idelsohn , Ruben D. Spies

This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…

Numerical Analysis · Mathematics 2017-11-08 Tianyu Qiu , Alexander Rieder , Francisco-Javier Sayas , Shougui Zhang

Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…

Analysis of PDEs · Mathematics 2024-12-23 S. G. Pyatkov , O. A. Soldatov

An analytic solution to a stationary heat conduction problem in 2D unbounded doubly periodic composite materials with temperature dependent conductivities of their components is given. Corresponding nonlinear boundary value problem is…

Analysis of PDEs · Mathematics 2014-04-01 David Kapanadze , Gennady Mishuris , Ekaterina Pesetskaya

The objective of this article is to introduce a novel technique for computing numerical solutions to the nonlinear inverse heat conduction problem. This involves solving nonlinear parabolic equations with Cauchy data provided on one side…

Numerical Analysis · Mathematics 2023-06-01 Dinh-Nho H`ao , Thuy T. Le , Loc H. Nguyen

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…

Analysis of PDEs · Mathematics 2007-05-23 Masaru Ikehata

We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…

Analysis of PDEs · Mathematics 2016-11-01 Ugur G. Abdulla

In this paper, we show that a hybrid method using coupled boundary measurements can determine electrical conductivity, thermal conductivity, and the product of heat capacity and heat density within a bounded domain on the plane uniquely up…

Analysis of PDEs · Mathematics 2017-02-01 Yifan Chang

We introduce a new method of solution for the convective heat transfer under forced laminar flow that is confined by two parallel plates with a distance of 2a or by a circular tube with a radius of a. The advection-conduction equation is…

Mathematical Physics · Physics 2018-08-30 Zhijie Xu

We present a numerical method for the solution of diffusion problems in unbounded planar regions with complex geometries of absorbing and reflecting bodies. Our numerical method applies the Laplace transform to the parabolic problem,…

Numerical Analysis · Mathematics 2024-08-19 Jesse Cherry , Alan E. Lindsay , Bryan D. Quaife

We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…

Analysis of PDEs · Mathematics 2020-02-24 Chifaa Ghanmi , Saloua Mani-Aouadi , Faouzi Triki

We describe the general setting for the optical Aharonov-Bohm effect based on the inverse problem of the identification of the coefficients of the governing hyperbolic equation by the boundary measurements. We interpret the inverse problem…

Mathematical Physics · Physics 2015-07-06 Gregory Eskin

In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…

Numerical Analysis · Mathematics 2018-07-04 Aihua Lin , Anastasiia Kuzmina , Per Kristen Jakobsen

We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…

Numerical Analysis · Mathematics 2025-03-25 Roman Chapko , Leonidas Mindrinos

This paper deals with the numerical methods for the reconstruction of source term in linear parabolic equation from final overdetermination. We assume that the source term has the form f(x)h(t) and h(t) is given, which guarantees the…

Analysis of PDEs · Mathematics 2014-02-19 Xiaoping Fang , Youjun Deng , Jing Li

We consider a boundary value problem in unbounded 2D doubly periodic composite with circular inclusions having arbitrary constant conductivities. By introducing complex potentials, the boundary value problem for the Laplace equation is…

Mathematical Physics · Physics 2013-08-27 David Kapanadze , Gennady Mishuris , Ekaterina Pesetskaya

There are two main approaches to solve inverse coefficient determination problems for wave equations: the Boundary Control method and an approach based on geometric optics. These notes focus on the Boundary Control method, but we will have…

Analysis of PDEs · Mathematics 2026-04-14 Medet Nursultanov , Lauri Oksanen

This paper proposes a new mathematical formulation for flow measurement based on the inverse source problem for wave equations with partial boundary measurement. Inspired by the design of acoustic Doppler current profilers (ADCPs), we…

Optimization and Control · Mathematics 2025-03-19 Jiwei Li , Lingyun Qiu , Zhongjing Wang , Hui Yu

We show that Boundary Control method, a method for hyperbolic inverse problems, is also capable of dealing directly with certain classes of elliptic and parabolic Inverse Boundary Value Problems; thus pointing towards Boundary Control…

General Mathematics · Mathematics 2025-04-10 Dimitra Kyriakopoulou

Inverse problems of recovering heat transfer coefficient from integral measurements are considered. The heat transfer coefficient occurs in the transmission conditions of imperfect contact type or the Robin type boundary conditions. It is…

Analysis of PDEs · Mathematics 2024-01-04 Sergey Grigorievich Pyatkov