Backward semi-linear parabolic equations with time-dependent coefficients and local Lipschitz source

DOI10.1088/1361-6420/aab8cbOpenAlexW2796719750MaRDI QIDQ4569358

Nguyen Van Duc, Nguyen Van Thang, Dinh Nho Hào

Publication date: 28 June 2018

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6420/aab8cb

zbMATH Keywords

Tikhonov regularizationill-posed problemsstability estimatelog-convexity methodbackward semi-linear parabolic equations

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

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Cites Work

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• The backward problem for Ginzburg-Landau-type equation
• Stability results for semi-linear parabolic equations backward in time
• Sharp estimates for approximations to a nonlinear backward heat equation
• An approximate solution for nonlinear backward parabolic equations
• A nonlinear parabolic equation backward in time: regularization with new error estimates
• Nonlinear diffusion-reaction problems with time-dependent diffusion coefficient
• Ginzburg-Landau phase transition theory and superconductivity
• On optimal regularization methods for the backward heat equation
• Stability estimates for a class of semi-linear ill-posed problems
• Compensating operators and stable backward in time marching in nonlinear parabolic equations
• On a backward parabolic problem with local Lipschitz source
• Control operators and iterative algorithms in variational data assimilation problems
• Stability results for backward parabolic equations with time-dependent coefficients
• Backward heat equations with locally lipschitz source
• Log-log convexity and backward uniqueness
• Regularization of parabolic equations backward in time by a non-local boundary value problem method
• Some backward uniqueness results
• Approximation of a parabolic non-linear evolution equation backwards in time
• Optimality for ill-posed problems under general source conditions
• Note on a regularization of a parabolic nonlinear evolution equation backwards in time
• Equations of parabolic type in a Banach space
• THE SOLVABILITY OF MIXED PROBLEMS FOR HYPERBOLIC AND PARABOLIC EQUATIONS
• Properties of solutions of ordinary differential equations in banach space