Abstract
We consider the unique continuation on a sphere for Helmholtz equation in three dimensions. A Hölder-type conditional stability is obtained. The numerical method is provided together with several numerical examples. The results in this paper may be applied to the study of inverse problems such as recovering far field scattering patterns with partial measurements.
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Acknowledgements
The authors thank the referee for useful comments. This work was supported by the National Science Foundation of China (No. 11971121).
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Chen, Y., Cheng, J. (2021). Unique Continuation on a Sphere for Helmholtz Equation and Its Numerical Treatments. In: Cheng, J., Dinghua, X., Saeki, O., Shirai, T. (eds) Proceedings of the Forum "Math-for-Industry" 2018. Mathematics for Industry, vol 35. Springer, Singapore. https://doi.org/10.1007/978-981-16-5576-0_7
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DOI: https://doi.org/10.1007/978-981-16-5576-0_7
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