Inverse Problems with Applications in Science and Engineering

1. Introduction. 1.1. Classification of inverse problems. 1.2. Systems of linear algebraic equations. 1.3. Regularization methods. 2. Inverse boundary-value problems. 2.1 Cauchy problem for the Laplace equation. 2.2. Cauchy problem for the Stokes system. 2.3. Cauchy-type problems for the biharmonic equation. 2.4. Cauchy problems for the heat equation. 2.5. Conclusions. 3. Inverse initial-value problems. 3.1. Quasi-reversibility methods. 3.2. Logarithmic convexity methods. 3.3. Non-local initial-value methods. 4. Space-dependent heat sources. 4.1. Space-dependent heat source identification. 4.2. Simultaneous identification of the space-dependent heat source and initial temperature. 5. Time-dependent heat sources. 5.1. Time-dependent heat source identification. 5.2. Non-local variants. 6. Space- and time-dependent sources. 6.1. Additive space- and time-dependent heat sources. 6.2. Additive space- and time-dependent heat sources. Integral observations. 6.3. Multiplicative space- and time-dependent source. 7. Inverse wave force problems. 7.1. Determination of a space-dependent force in the one-dimensional wave equation from Cauchy data. 7.2. Determination of the force function in the multi-dimensional wave equation from Cauchy data. 7.3. Determination of a space-dependent force function from final or time-averaged displacement data. 8. Reconstruction of interfacial coefficients. 8.1. Introduction. 8.2. Mathematical formulation. 8.3. Conjugate gradient method (CGM). 8.4. Numerical results and discussions. 9. Identification of constant parameters in diffusion. 9.1. Homogeneous and isotropic diffusion. 9.2. A two-dimensional tracer dispersion problem. 9.3. Determination of constant thermal properties. 10. Time-dependent conductivity. 10.1. Identification of the time-dependent conductivity. 10.2. Identification of the time-dependent conductivity of an inhomogeneous diffusive material. 10.3. Finding the time-dependent diffusion coefficient from an integral observation. 11. Space-dependent conductivity. 11.1. Reconstruction of a permeability function from core measurements and pressure data. 11.2. Discontinuous anisotropic conductivity. 11.3. Reconstruction of an orthotropic conductivity. 12. Nonlinear conductivity. 12.1. Determination of nonlinear thermal properties. 12.2. Nonlinear and heterogeneous conductivity. 13. Anti-reflection coatings. 13.1. Mathematical model and analysis. 13.2. Numerical implementation. 13.3. Conclusions. 14. Flexural rigidity of a beam. 14.1. Distributed parameters in beam-type systems. 14.2. The comparison model method. 14.3. Determination of the flexural rigidity of a beam from limited boundary measurements.