Uniqueness results in the identification of distributed sources over Germain–Lagrange plates by boundary measurements

Abstract

We prove that the loading composed by a finite sum of time-independent sources acting over a bounded plate can be uniquely identified by knowing the normal derivative of the displacement along a subset of the boundary or the displacement of the points in a certain set near the boundary. This is true even if these data correspond to an arbitrary small interval of time. The method used is to reduce the problem to another one for the wave equation.

Keywords:

• Inverse problems
• partial differential equations
• wave equation
• Germain–Lagrange plate equation

AMS Subject Classifications:

• 35R30; 74K20; 35Q74

Acknowledgements

The author wishes to thank Professor Paulo D. Cordaro from the University of Sao Paulo for his always constructive comments and the anonymous reviewers that made suggestions to improve the article.

Notes

No potential conflict of interest was reported by the author.

1 Here regular means that locally is on one side of .

Additional information

Funding

This work was partially supported by Fapesp [Proj. 2013/20305-0] and CNPq [Proc. 304972/2013-4].