Determination of a time-dependent term in the right-hand side of linear parabolic equations

DOI10.1007/S40306-015-0143-YzbMath1347.65151OpenAlexW861047215MaRDI QIDQ300669

Nguyen Thi Ngoc Oanh, Bui Viet Huong

Publication date: 28 June 2016

Published in: Acta Mathematica Vietnamica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40306-015-0143-y

zbMATH Keywords

numerical examplesconjugate gradient methoddetermination of heat sourcesinverse problems in heat transferspiliting method

Mathematics Subject Classification ID

Heat equation (35K05) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Iterative numerical methods for linear systems (65F10) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

Related Items (9)

Determination of a term in the right-hand side of parabolic equations ⋮ Determination of the initial condition in parabolic equations from integral observations ⋮ On the inverse problem for one-dimensional Burgers' equation from the interior observation ⋮ The necessary optimal condition of inverse heat source problem ⋮ Identifying an unknown source term in a heat equation with time-dependent coefficients ⋮ Existence of optimal solution to the problem of finding an initial condition for nonlinear diffusion from integral observations ⋮ Determination of an unknown time-dependent heat source from a nonlocal measurement by finite difference method ⋮ On stability and regularization for data-driven solution of parabolic inverse source problems ⋮ A method for choosing the regularization parameter of determining the right-hand side from integral observation

Cites Work

• Identification of an unknown time-dependent heat source term from overspecified Dirichlet boundary data by conjugate gradient method
• Splitting-based conjugate gradient method for a multi-dimensional linear inverse heat conduction problem
• The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
• A variational discretization concept in control constrained optimization: The linear-quadratic case
• Numerical solution of the inverse problem of reconstructing a distributed right-hand side of a parabolic equation
• The boundary-element method for the determination of a heat source dependent on one variable
• A noncharacteristic cauchy problem for linear parabolic equations II: a variational method
• A noncharacteristic cauchy problem for linear parabolic equations III: a variational method and its approximation schemes
• Inverse problem for a parabolic equation with integral overdetermination
• The regularizing properties of the adjoint gradient method in ill-posed problems
• On problems of determining the source function in a parabolic equation
• Determination of an Unknown Heat Source from Overspecified Boundary Data
• Inverse problems for partial differential equations
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