LOCAL EXISTENCE AND GLOBAL UNIQUENESS IN ONE DIMENSIONAL NONLINEAR HYPERBOLIC INVERSE PROBLEMS

Abstract

We prove local existence and global uniqueness in one dimensional nonlinear hyperbolic inverse problems. The basic key for showing the local existence of inverse solution is the principle of contracted mapping. As an application, we consider a hyperbolic inverse problem with damping term.

Keywords

• nonlinear hyperbolic inverse problems;
• local existence;
• global uniqueness;
• the principle of contracted mapping

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References

1. Inverse problems in vibration G.M.L. Gladwell
2. Applied Math-ematical Sciences v.127 Inverse Problems for Partial Differential Equations V. Isakov
3. Soviet Math. Dokl v.38 On stability estimates in multidimensional inverse problems for differential equations (English translation) A. Khaidarov
4. Inverse Problems v.8 Inverse problems and Carleman estimates M.V. Klibanov https://doi.org/10.1088/0266-5611/8/4/009
5. Translations AMS, Pro-bidence, R.I. v.130 One-dimensional inverse problems of mathematical physics M.M. Lavrent'ev;K.G. Reznitskaya;V.G. Yakhno
6. Commun. in Partial Differential Equations v.13 Uniqueness for an inverse problem for the wave equation Rakesh;Symes https://doi.org/10.1080/03605308808820539
7. Integral Geometry and Inverse Problems for Hyperbolic Equa-tions V.G. Romanov
8. Inverse Problems of Mathematical Physics, (English translation)
9. translation in Differential Equations v.25 no.2 Local solvability of some multidimens
10. J. Math. Pures. Appl. v.78 Uniqueness and stability in multidimensional hyperbolic inverse problems M. Yamamoto https://doi.org/10.1016/S0021-7824(99)80010-5