Determination of the initial density in nonlocal diffusion from final time measurements

DOI10.3934/dcdss.2022029zbMath1491.35460OpenAlexW4213438288MaRDI QIDQ2673673

Mourad Hrizi, Maatoug Hassine, Mohamed Oudi Bensalah

Publication date: 10 June 2022

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2022029

zbMATH Keywords

numerical simulationsoptimization problemreconstruction algorithmnonlocal operatorfractional diffusion equation

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Initial-boundary value problems for second-order parabolic equations (35K20) Inverse problems for PDEs (35R30) Iterative numerical methods for linear systems (65F10) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Fractional partial differential equations (35R11)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations
• Determination of the initial condition in parabolic equations from boundary observations
• Identification of the zeroth-order coefficient in a time fractional diffusion equation
• A splitting method for a backward parabolic equation with time-dependent coefficients
• Hitchhiker's guide to the fractional Sobolev spaces
• Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
• Nonlocal problems with Neumann boundary conditions
• Eigenvalues of the fractional Laplace operator in the interval
• An introduction to Sobolev spaces and interpolation spaces
• Estimates of initial conditions of parabolic equations and inequalities in infinite domains via lateral Cauchy data
• Functional analysis, Sobolev spaces and partial differential equations
• Finite element approximation for the fractional eigenvalue problem
• A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
• Inverse source problem for a space-time fractional diffusion equation
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• Identifying an unknown source term in a time-space fractional parabolic equation
• The fractional Landweber method for identifying the space source term problem for time-space fractional diffusion equation
• The Calderón problem for the fractional Schrödinger equation with drift
• Stable reconstruction of the initial condition in parabolic equations from boundary observations
• What is the fractional Laplacian? A comparative review with new results
• Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications
• Local density of solutions to fractional equations
• Finite element approximations for fractional evolution problems
• Carleman estimates for the regularization of ill-posed Cauchy problems
• Local approximation of arbitrary functions by solutions of nonlocal equations
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• The extremal solution for the fractional Laplacian
• Conditional stability and numerical reconstruction of initial temperature
• Inverse space-dependent source problem for a time-fractional diffusion equation by an adjoint problem approach
• An ill-posed problem for the Black–Scholes equation for a profitable forecast of prices of stock options on real market data
• An inverse time-dependent source problem for a time-fractional diffusion equation
• From the long jump random walk to the fractional Laplacian
• Variational Analysis in Sobolev and BV Spaces
• A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
• Stability results for backward parabolic equations with time-dependent coefficients
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Regularization of parabolic equations backward in time by a non-local boundary value problem method
• Regularity theory for fully nonlinear integro-differential equations
• Global Convergence Properties of Conjugate Gradient Methods for Optimization
• Error Estimates for the Optimal Control of a Parabolic Fractional PDE
• Inverse source problem for a diffusion equation involving the fractional spectral Laplacian
• Recovering the source and initial value simultaneously in a parabolic equation
• Monotonicity-Based Inversion of the Fractional Schrödinger Equation II. General Potentials and Stability
• Monotonicity-based Inversion of the Fractional Schrödinger Equation I. Positive Potentials
• Estimates of initial conditions of parabolic equations and inequalities via lateral Cauchy data
• Function minimization by conjugate gradients
• Determination of the initial condition in parabolic equations from integral observations
• On the Dirichlet problem for second-order elliptic integro-differential equations
• The Conjugate Gradient Method for Linear and Nonlinear Operator Equations
• Numerical methods for fractional diffusion