Determination of the initial condition in parabolic equations from integral observations

DOI10.1080/17415977.2016.1229778zbMath1369.65116OpenAlexW2520733674MaRDI QIDQ5348719

Nguyen Thi Ngoc Oanh, Dinh Nho Hào

Publication date: 18 August 2017

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

Full work available at URL: https://doi.org/10.1080/17415977.2016.1229778

zbMATH Keywords

regularizationconjugate gradient methodsingular valuesparabolic equationsill-posed problemssplitting methodintegral observationsdetermining the initial condition

Mathematics Subject Classification ID

Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (9)

Determination of the initial density in nonlocal diffusion from final time measurements ⋮ A numerical method for an inverse source problem for parabolic equations and its application to a coefficient inverse problem ⋮ On the inverse problem for one-dimensional Burgers' equation from the interior observation ⋮ Stable reconstruction of the initial condition in parabolic equations from boundary observations ⋮ A two-dimensional backward heat problem with statistical discrete data ⋮ Existence of optimal solution to the problem of finding an initial condition for nonlinear diffusion from integral observations ⋮ On recovering parabolic diffusions from their time-averages ⋮ \(l^1\)-weighted regularization for the problem of recovering sparse initial conditions in parabolic equations from final measurements ⋮ A method for choosing the regularization parameter of determining the right-hand side from integral observation

Cites Work

• Determination of a time-dependent term in the right-hand side of linear parabolic equations
• A splitting method for a backward parabolic equation with time-dependent coefficients
• Splitting-based conjugate gradient method for a multi-dimensional linear inverse heat conduction problem
• A variational discretization concept in control constrained optimization: The linear-quadratic case
• Carleman estimates for the regularization of ill-posed Cauchy problems
• An ill-posed problem for the Black–Scholes equation for a profitable forecast of prices of stock options on real market data
• Stability results for backward parabolic equations with time-dependent coefficients
• 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
• A boundary element method for a multi-dimensional inverse heat conduction problem

This page was built for publication: Determination of the initial condition in parabolic equations from integral observations