Fréchet differentiability in Besov spaces in the optimal control of parabolic free boundary problems

DOI10.1515/jiip-2017-0014zbMath1390.35409OpenAlexW3098383917MaRDI QIDQ1746499

Jonathan M. Goldfarb, Ugur G. Abdulla

Publication date: 25 April 2018

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip-2017-0014

zbMATH Keywords

Fréchet differentiabilityBesov spacesembedding theoremsparabolic free boundary probleminverse Stefan problemoptimal control of parabolic PDEtrace embeddings

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Inverse problems for PDEs (35R30) Free boundary problems for PDEs (35R35)

Related Items (7)

Discretization and convergence of the EIT optimal control problem in Sobolev spaces with dominating mixed smoothness ⋮ Gradient method in Hilbert-Besov spaces for the optimal control of parabolic free boundary problems ⋮ An instantaneous semi-Lagrangian approach for boundary control of a melting problem. ⋮ Optimal Stefan problem ⋮ Optimal control of multiphase free boundary problems for nonlinear parabolic equations ⋮ Optimal control of coefficients in parabolic free boundary problems modeling laser ablation ⋮ Optimal control of the multiphase Stefan problem

Cites Work

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• On the optimal control of the free boundary problems for the second order parabolic equations. II. Convergence of the method of finite differences
• The Cauchy problem for a linear parabolic partial differential equation
• The inverse Stefan problem as a problem of nonlinear approximation theory
• General free-boundary problems for the heat equation. I
• The numerical solution of the inverse Stefan problem
• On the optimal control of the free boundary problems for the second order parabolic equations. I: Well-posedness and convergence of the method of lines
• A Cauchy problem for the heat equation
• The combined use of a nonlinear chernoff formula with a regularization procedure for two-phase stefan problems
• Numerical Approximation of a Cauchy Problem for a Parabolic Partial Differential Equation
• The Noncharacteristic Cauchy Problem for a Class of Equations with Time Dependence. I. Problems in One Space Dimension
• Determining Surface Temperatures from Interior Observations
• Real-time control of the free boundary in a two-phase stefan problem
• The Cauchy Problem for the Heat Equation
• General One-Phase Stefan Problems and Free Boundary Problems for the Heat Equation with Cauchy Data Prescribed on the Free Boundary
• Wave height and wave resistance in the presence of a viscous wake

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