Abstract
As previously mentioned, for problems in mathematical physics Hadamard [63] postulated three requirements: a solution should exist, the solution should be unique, and the solution should depend continuously on the data. The third postulate is motivated by the fact that in all applications the data will be measured quantities. Therefore, one wants to make sure that small errors in the data will cause only small errors in the solution. A problem satisfying all three requirements is called well-posed. Otherwise, it is called ill-posed. As shown in the previous chapter, the direct obstacle scattering problem is well-posed.
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© 1992 Springer-Verlag Berlin Heidelberg
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Colton, D., Kress, R. (1992). Ill-Posed Problems. In: Inverse Acoustic and Electromagnetic Scattering Theory. Applied Mathematical Sciences, vol 93. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02835-3_4
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DOI: https://doi.org/10.1007/978-3-662-02835-3_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-02837-7
Online ISBN: 978-3-662-02835-3
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