Approximate Solutions of Inverse Problems for Nonlinear Space Fractional Diffusion Equations with Randomly Perturbed Data

DOI10.1137/17M1111139zbMath1384.35146arXiv1611.01876MaRDI QIDQ4636375

Nguyen Huy Tuan, Erkan Nane

Publication date: 19 April 2018

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.01876

zbMATH Keywords

approximate solutionstruncation methodinverse problem for fractional heat equationrandomly perturbed final valuerandomly perturbed source

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Fractional partial differential equations (35R11)

Related Items (13)

On a nonlinear parabolic equation with fractional Laplacian and integral conditions ⋮ Terminal value problem for nonlinear parabolic equation with Gaussian white noise ⋮ On the inverse problem for nonlinear strongly damped wave equations with discrete random noise ⋮ Inverse problems for heat equation and space-time fractional diffusion equation with one measurement ⋮ On a non-local Sobolev-Galpern-type equation associated with random noise ⋮ Approximate solution of the backward problem for Kirchhoff's model of parabolic type with discrete random noise ⋮ On a backward problem for multidimensional Ginzburg–Landau equation with random data ⋮ Final value problem for nonlinear time fractional reaction-diffusion equation with discrete data ⋮ A two-dimensional sideways problem with random discrete data ⋮ On Cauchy problem for nonlinear fractional differential equation with random discrete data ⋮ An approximate solution for a nonlinear biharmonic equation with discrete random data ⋮ Analysis of a quasi-reversibility method for nonlinear parabolic equations with uncertainty data ⋮ On a stochastic nonclassical diffusion equation with standard and fractional Brownian motion

Uses Software

• Ziggurat
• rnorrexp

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Inverse source problem for time-fractional diffusion with discrete random noise
• Space-time fractional diffusion on bounded domains
• A new Fourier truncated regularization method for semilinear backward parabolic problems
• Some extended results on a nonlinear ill-posed heat equation and remarks on a general case of nonlinear terms
• A two-dimensional backward heat problem with statistical discrete data
• A new general filter regularization method for Cauchy problems for elliptic equations with a locally Lipschitz nonlinear source
• An approximate solution for nonlinear backward parabolic equations
• Stability estimates for a class of semi-linear ill-posed problems
• Generalized quasi-reversibility method for a backward heat equation with a fractional Laplacian
• On a backward parabolic problem with local Lipschitz source
• A nonlinear case of the 1-D backward heat problem: regularization and error estimate
• Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise
• Nonparametric statistical inverse problems
• Statistical inference for inverse problems
• Digital Removal of Random Media Image Degradations by Solving the Diffusion Equation Backwards in Time
• Statistical Inverse Estimation in Hilbert Scales
• Nonparametric regression in a statistical modified Helmholtz equation using the Fourier spectral regularization
• Analysis of regularized inversion of data corrupted by white Gaussian noise
• An introduction to the mathematical theory of inverse problems

This page was built for publication: Approximate Solutions of Inverse Problems for Nonlinear Space Fractional Diffusion Equations with Randomly Perturbed Data