Determination of the initial density in nonlocal diffusion from final time measurements
From MaRDI portal
Publication:2673673
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
numerical simulationsoptimization problemreconstruction algorithmnonlocal operatorfractional diffusion equation
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
