Introduction to Inverse Problems for Differential Equations

DOI10.1007/978-3-319-62797-7zbMath1385.65053OpenAlexW2740844058MaRDI QIDQ4976862

Alemdar Hasanov Hasanoglu, Vladimir G. Romanov

Publication date: 2 August 2017

Full work available at URL: https://doi.org/10.1007/978-3-319-62797-7

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Inverse problems for PDEs (35R30) Radon transform (44A12) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Nonlinear ill-posed problems (47J06) Inverse problems involving ordinary differential equations (34A55) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems in thermodynamics and heat transfer (80A23) Linear operators and ill-posed problems, regularization (47A52) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Numerical solution to inverse problems in abstract spaces (65J22) Maxwell equations (35Q61)

Related Items (51)

Identification of a space- and time-dependent source in a variable coefficient advection-diffusion equation from Dirichlet and Neumann boundary measured outputs ⋮ An approximate method for solving the inverse coefficient problem ⋮ On the randomised stability constant for inverse problems ⋮ Uniqueness and numerical reconstruction for inverse problems dealing with interval size search ⋮ An optimization algorithm for determining a point heat source position in a 2D domain using a hybrid metaheuristic ⋮ Lipschitz continuity of the Fréchet gradient in an inverse coefficient problem for a parabolic equation with Dirichlet measured output ⋮ Inverse Problems of Finding the Lowest Coefficient in the Elliptic Equation ⋮ On unique determination of an unknown spatial load in damped Euler-Bernoulli beam equation from final time output ⋮ An inverse problem of reconstructing the time-dependent coefficient in a one-dimensional hyperbolic equation ⋮ Identification of a harmonically varying external source in wave equation from Neumann-type boundary measurement ⋮ Simultaneously identifying the thermal conductivity and radiative coefficient in heat equation from Dirichlet and Neumann boundary measured outputs ⋮ Uniqueness and stability analysis of final data inverse source problems for evolution equations ⋮ Inverse problem of determining the source in the Aller-Lykov equation with a final redefinition ⋮ Inverse problem for an integrodifferential equation of the hyperbolic type in a rectangular domain ⋮ A gradient-based approach for identification of the zeroth-order coefficient \(p(x)\) in the parabolic equation \(u_t=(k(x)u_x)_x-p(x)u\) from Dirichlet-type measured output ⋮ Parameter estimation inspired by temperature measurements for a chemotactic model of honeybee thermoregulation ⋮ Inference for a discretized stochastic logistic differential equation and its application to biological growth ⋮ INVERSE PROBLEMS OF RESTORING PARAMETERS IN PARABOLIC AND HYPERBOLIC EQUATIONS ⋮ Reconstruction of the spatial component in the source term of a vibrating elastic plate from boundary observation ⋮ Inverse coefficient problem for the time‐fractional diffusion equation with Hilfer operator ⋮ Identification of source terms in heat equation with dynamic boundary conditions ⋮ Determining the coefficient of a mixed parabolic-hyperbolic equation with noncharacteristic type change line ⋮ Numerical Reconstruction of Radiative Sources from Partial Boundary Measurements ⋮ PinT Preconditioner for Forward-Backward Evolutionary Equations ⋮ Solution of the backward problem for the space-time fractional diffusion equation related to the release history of a groundwater contaminant ⋮ On the solvability of the inverse problems of parameter recovery in elliptic equations ⋮ Inverse source problem for the equation of forced vibrations of a beam ⋮ Unnamed Item ⋮ Recovering a potential in damped wave equation from Neumann-to-Dirichlet operator ⋮ PDE-based numerical method for a limited angle x-ray tomography ⋮ An inverse source problem for singular parabolic equations with interior degeneracy ⋮ Inverse problem for elastic body with thin elastic inclusion ⋮ Identification of the diffusion coefficient in a time fractional diffusion equation ⋮ An inverse problem for the KdV equation with Neumann boundary measured data ⋮ Identification of a temporal load in a cantilever beam from measured boundary bending moment ⋮ Identification of an unknown shear force in a cantilever Euler-Bernoulli beam from measured boundary bending moment ⋮ Reconstruction of the principal coefficient in the damped wave equation from Dirichlet-to-Neumann operator ⋮ Some properties of the potential-to-ground state map in quantum mechanics ⋮ On the shape differentiability of objectives: a Lagrangian approach and the Brinkman problem ⋮ Simultaneous reconstruction of time-dependent coefficients in the parabolic equation from over-specification conditions ⋮ Inverse source problem in a space fractional diffusion equation from the final overdetermination. ⋮ Infinite-dimensional inverse problems with finite measurements ⋮ Identification of an unknown shear force in the Euler–Bernoulli cantilever beam from measured boundary deflection ⋮ Some inverse problems for the Burgers equation and related systems ⋮ Calculation of the gradient of Tikhonov's functional in solving coefficient inverse problems for linear partial differential equations ⋮ Unique recovery of unknown spatial load in damped Euler–Bernoulli beam equation from final time measured output ⋮ Calculating heat and wave propagation from the lateral Cauchy data ⋮ Coupling RBF-based meshless method and Landweber iteration algorithm for approximating a space-dependent source term in a time fractional diffusion equation ⋮ Recovering a potential in damped wave equation from Dirichlet-to-Neumann operator ⋮ Determination of a time-dependent potential in the higher-order pseudo-hyperbolic problem ⋮ Determination of thermophysical characteristics in a nonlinear inverse heat transfer problem

This page was built for publication: Introduction to Inverse Problems for Differential Equations