A Riesz–Feller space‐fractional backward diffusion problem with a time‐dependent coefficient: regularization and error estimates

DOI10.1002/MMA.4284zbMath1372.35347OpenAlexW2576674382MaRDI QIDQ5280156

Duong Dang Xuan Thanh, Dinh Nguyen Duy Hai, Nguyen Huy Tuan, Dang Duc Trong

Publication date: 20 July 2017

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.4284

zbMATH Keywords

regularizationerror estimateill-posed problemspace-fractional backward diffusion problem

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Heat equation (35K05) Ill-posed problems for PDEs (35R25) Linear operators and ill-posed problems, regularization (47A52) Fractional partial differential equations (35R11)

Related Items (4)

Weak solution to a Robin problem of anomalous diffusion equations: Uniqueness and stable algorithm for the TPC system ⋮ On the well-posedness of a spectral fractional forward-backward pseudo-parabolic equation ⋮ Recovering the historical distribution for nonlinear space-fractional diffusion equation with temporally dependent thermal conductivity in higher dimensional space ⋮ Quasi solution of a backward space fractional diffusion equation

Cites Work

• On a Riesz-Feller space fractional backward diffusion problem with a nonlinear source
• A new \textit{a posteriori} parameter choice strategy for the convolution regularization of the space-fractional backward diffusion problem
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Some recent advances in theory and simulation of fractional diffusion processes
• Optimal Discretization of Inverse Problems in Hilbert Scales. Regularization and Self-Regularization of Projection Methods
• Two regularization methods for solving a Riesz–Feller space-fractional backward diffusion problem
• Regularization under general noise assumptions
• A regularization for a Riesz–Feller space-fractional backward diffusion problem
• Geometry of linear ill-posed problems in variable Hilbert scales
• The fundamental solution of the space-time fractional diffusion equation
• An inverse problem for space‐fractional backward diffusion problem

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