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27 results on '"Hu, Guanghui"'

5. Inverse moving source problem for time-fractional evolution equations : determination of profiles

Author

Liu, Yikan, Hu, Guanghui, Yamamoto, Masahiro, Liu, Yikan, Hu, Guanghui, and Yamamoto, Masahiro

Abstract

This article is concerned with two inverse problems on determining moving source profile functions in evolution equations with a derivative order alpha is an element of (0, 2] in time. In the first problem, the sources are supposed to move along known straight lines, and we suitably choose partial interior observation data in finite time. Reducing the problems to the determination of initial values, we prove the unique determination of one and two moving source profiles for 0 < alpha <= 1 and 1 < alpha <= 2, respectively. In the second problem, the orbits of moving sources are assumed to be known, and we consider the full lateral Cauchy data. At the cost of infinite observation time, we prove the unique determination of one moving source profile by constructing test functions.

Published
2021

6. Inverse moving source problem for time-fractional evolution equations : determination of profiles

Author

1000070773084, Liu, Yikan, Hu, Guanghui, 1000050182647, Yamamoto, Masahiro, 1000070773084, Liu, Yikan, Hu, Guanghui, 1000050182647, and Yamamoto, Masahiro

Abstract

This article is concerned with two inverse problems on determining moving source profile functions in evolution equations with a derivative order alpha is an element of (0, 2] in time. In the first problem, the sources are supposed to move along known straight lines, and we suitably choose partial interior observation data in finite time. Reducing the problems to the determination of initial values, we prove the unique determination of one and two moving source profiles for 0 < alpha <= 1 and 1 < alpha <= 2, respectively. In the second problem, the orbits of moving sources are assumed to be known, and we consider the full lateral Cauchy data. At the cost of infinite observation time, we prove the unique determination of one moving source profile by constructing test functions.

Published
2021

27. Some inverse problems arising from elastic scattering by rigid obstacles.

Author

Hu, Guanghui, Kirsch, Andreas, and Sini, Mourad

Subjects
*SHEAR waves, *MATHEMATICAL decoupling, *FACTORIZATION, *POLYHEDRA, *LIPSCHITZ spaces, *INTERNAL friction
Abstract

In the first part of this paper, it is proved that a C2-regular rigid scatterer in can be uniquely identified by the shear part (i.e. S-part) of the far-field pattern corresponding to all incident shear waves at any fixed frequency. The proof is short and it is based on a kind of decoupling of the S-part of scattered wave from its pressure part (i.e. P-part) on the boundary of the scatterer. Moreover, uniqueness using the S-part of the far-field pattern corresponding to only one incident plane shear wave holds for a ball or a convex Lipschitz polyhedron. In the second part, we adapt the factorization method to recover the shape of a rigid body from the scattered S-waves (resp. P-waves) corresponding to all incident plane shear (resp. pressure) waves. Numerical examples illustrate the accuracy of our reconstruction in . In particular, the factorization method also leads to some uniqueness results for all frequencies excluding possibly a discrete set. [ABSTRACT FROM AUTHOR]

Published
2013
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