A new algorithm to determine the creation or depletion term of parabolic equations from boundary measurements

DOI10.1016/j.camwa.2020.09.010zbMath1454.65107arXiv1906.01931OpenAlexW3087916579MaRDI QIDQ2212326

Loc Hoang Nguyen

Publication date: 20 November 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.01931

zbMATH Keywords

approximationFourier coefficientsparabolic equationscoefficient inverse problem

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Heat equation (35K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods for boundary value problems involving PDEs (65N06) Physiological flow (92C35) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Overdetermined initial value problems for PDEs and systems of PDEs (35N20)

Related Items (10)

Global reconstruction of initial conditions of nonlinear parabolic equations via the Carleman-contraction method ⋮ Reconstructing a space-dependent source term via the quasi-reversibility method ⋮ The gradient descent method for the convexification to solve boundary value problems of quasi-linear PDEs and a coefficient inverse problem ⋮ Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data ⋮ The Carleman contraction mapping method for quasilinear elliptic equations with over-determined boundary data ⋮ Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations by partial boundary layer data. Part II: Some inverse problems ⋮ The quasi-reversibility method to numerically solve an inverse source problem for hyperbolic equations ⋮ Simultaneous reconstruction of time-dependent coefficients in the parabolic equation from over-specification conditions ⋮ A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications ⋮ The Carleman-based contraction principle to reconstruct the potential of nonlinear hyperbolic equations

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