5 Convexification for ill-posed Cauchy problems for quasi-linear PDEs

Chapters in this book

1. Frontmatter I
2. Preface VII
3. Acknowledgments IX
4. Contents XI
5. 1 Topics of this book 1
6. 2 Carleman estimates and Hölder stability for ill-posed Cauchy problems 7
7. 3 Global uniqueness for coefficient inverse problems and Lipschitz stability for a hyperbolic CIP 41
8. 4 The quasi-reversibility numerical method for ill-posed Cauchy problems for linear PDEs 77
9. 5 Convexification for ill-posed Cauchy problems for quasi-linear PDEs 93
10. 6 A special orthonormal basis in L₂(a, b) for the convexification for CIPs without the initial conditions—restricted Dirichlet-to-Neumann map 121
11. 7 Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data 139
12. 8 Convexification for a coefficient inverse problem for a hyperbolic equation with a single location of the point source 171
13. 9 Convexification for an inverse parabolic problem 199
14. 10 Experimental data and convexification for the recovery of the dielectric constants of buried targets using the Helmholtz equation 229
15. 11 Travel time tomography with formally determined incomplete data in 3D 263
16. 12 Numerical solution of the linearized travel time tomography problem with incomplete data 291
17. Bibliography 311
18. Index 323