A collage-based approach to solving inverse problems for second-order nonlinear parabolic PDEs

DOI10.1016/j.jmaa.2013.04.046zbMath1435.35417OpenAlexW288621542MaRDI QIDQ2257549

Yanyan Li

Publication date: 25 February 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2013.04.046

zbMATH Keywords

optimizationparameter estimationinverse problemsnonlinearpartial differential equationsparabolic

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Inverse problems for PDEs (35R30) Semilinear parabolic equations (35K58)

Related Items (7)

Extensions of the Lax-Milgram theorem to Hilbert \(C^*\)-modules ⋮ Using the generalized collage theorem for estimating unknown parameters in perturbed mixed variational equations ⋮ Galerkin schemes and inverse boundary value problems in reflexive Banach spaces ⋮ Fractal-based methods and inverse problems for differential equations: current state of the art ⋮ Galerkin method for constrained variational equations and a collage-based approach to related inverse problems ⋮ Convergence and Data Dependency of Normal−S Iterative Method for Discontinuous Operators on Banach Space ⋮ Numerical solution for an inverse variational problem

Cites Work

• A generalized collage method based upon the Lax-Milgram functional for solving boundary value inverse problems
• Using the collage method to solve one-dimensional two-point boundary value problems at steady-state
• Applied functional analysis. Applications to mathematical physics. Vol. 1
• Fractal-Based Methods in Analysis
• Solution of an inverse problem for fractals and other sets
• Solving inverse problems for ordinary differential equations using the Picard contraction mapping
• Solving an inverse problem for Urison-type integral equations using Banach s fixed point theorem
• Solving inverse two-point boundary value problems using collage coding
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