An approach to numerical solution of some inverse problems for parabolic equations

DOI10.1080/17415977.2013.827184zbMath1312.65150OpenAlexW2013812642MaRDI QIDQ5496489

Kamil R. Aida-zade, A. B. Rahimov

Publication date: 2 February 2015

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2013.827184

zbMATH Keywords

numerical exampleinverse problemfinite difference methodparabolic equationmethod of linesinverse source problemnonlocal conditions

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Inverse problems for PDEs (35R30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

Related Items (9)

A fourth-order compact difference scheme for the parabolic inverse problem with an overspecification at a point ⋮ On approximation of coefficient inverse problems for differential equations in functional spaces ⋮ Solution to a class of inverse problems for a system of loaded ordinary differential equations with integral conditions ⋮ Numerical solution to a class of inverse problems for parabolic equation ⋮ On recovering space or time-dependent source functions for a parabolic equation with nonlocal conditions ⋮ Identification of piecewise constant filtration parameters and boundaries of their constancy domains ⋮ Identification of the potential coefficient in the Schrödinger equation with incomplete initial conditions from a boundary observation ⋮ On the numerical solution to an inverse problem of recovering a source of special type in a parabolic equation ⋮ Numerical solution to inverse problems of recovering special-type source of a parabolic equation

Cites Work

• Unnamed Item
• The method of central difference for the inverse time-dependent heat source problem
• Determination of a time-dependent heat source under nonlocal boundary and integral overdetermination conditions
• The method of fundamental solutions for the inverse heat source problem
• An inverse source problem with single Dirichlet type measured output data for a linear parabolic equation
• Two regularization methods to identify time-dependent heat source through an internal measurement of temperature
• A two-stage LGSM to identify time-dependent heat source through an internal measurement of temperature
• Optimization method for the inverse problem of reconstructing the source term in a parabolic equation
• On the problem of identification of a coefficient in a parabolic equation
• A Lie-group shooting method for reconstructing a past time-dependent heat source
• Inverse and ill-posed problems. Theory and applications.
• Determination of a spacewise dependent heat source
• The boundary-element method for the determination of a heat source dependent on one variable
• Numerical solution of the inverse problem of determining an unknown source term in a two-dimensional heat equation
• The method of fundamental solutions for the inverse space-dependent heat source problem
• ON CERTAIN INVERSE PROBLEMS FOR PARABOLIC EQUATIONS WITH FINAL AND INTEGRAL OBSERVATION
• Structural identification of an unknown source term in a heat equation
• Numerical method of identification of dynamic system parameters
• On the transfer of boundary conditions for systems of ordinary linear differential equations (a variant of the dispersive method)
• A variational method for identifying a spacewise-dependent heat source
• Identification of source locations in two-dimensional heat equations
• Some inverse problems for strong parabolic systems

This page was built for publication: An approach to numerical solution of some inverse problems for parabolic equations