Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift

DOI10.1088/1361-6420/abe6f0zbMath1475.35432arXiv2012.11042OpenAlexW3129365634MaRDI QIDQ5854068

Yuxuan Gong, Xiang Xu, Peijun Li, Xu Wang

Publication date: 15 March 2021

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

Full work available at URL: https://arxiv.org/abs/2012.11042

zbMATH Keywords

convex optimizationdiscrete Fourier transformsemi-definite programmingregularization methodCaputo fractional derivativetime-fractional diffusion equationphase retrieval problemPhaseLift method

Mathematics Subject Classification ID

Random fields (60G60) Convex programming (90C25) Numerical methods based on nonlinear programming (49M37) Initial-boundary value problems for second-order parabolic equations (35K20) Brownian motion (60J65) Fractional derivatives and integrals (26A33) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) White noise theory (60H40) Numerical methods for discrete and fast Fourier transforms (65T50) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) 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) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (5)

An inverse potential problem for the stochastic diffusion equation with a multiplicative white noise ⋮ Well-posedness of the stochastic time-fractional diffusion and wave equations and inverse random source problems ⋮ Stability of inverse random source scattering problems in a multi-layered medium ⋮ The backward problem of stochastic convection-diffusion equation ⋮ Estimating the memory parameter for potentially non-linear and non-Gaussian time series with wavelets

Uses Software

• TFOCS
• PhaseLift

Cites Work

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