On the inverse problem for one-dimensional Burgers' equation from the interior observation

DOI10.1007/s41808-023-00244-6zbMath1526.35321OpenAlexW4386443062MaRDI QIDQ6058389

Nguyen Thi Ngoc Oanh

Publication date: 1 November 2023

Published in: Journal of Elliptic and Parabolic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41808-023-00244-6

zbMATH Keywords

conjugate gradient methodBurgers' equationvariational methodnecessary optimality conditioninterior observation

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems in optimal control (49N45) Semilinear parabolic equations (35K58)

Cites Work

• Determination of a time-dependent term in the right-hand side of linear parabolic equations
• The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
• Analysis of instantaneous control for the Burgers equation
• Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
• Stability estimates for Burgers-type equations backward in time
• Asymptotic behavior of solutions to the viscous Burgers equation
• Exact and numerical solutions for non-linear Burger's equation by VIM
• Control operators and iterative algorithms in variational data assimilation problems
• A novel approach to Burgers' equation
• The Laplace transform method for Burgers' equation
• Adjoint Equations and Perturbation Algorithms in Nonlinear Problems
• Determination of the initial condition in parabolic equations from integral observations
• Iterative methods for data assimilation for Burgers' equation
• The partial differential equation u_t + uu_x = μ_xx
• A semilinear problem related to Burgers' equation
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