Abstract
An exposition is given of the abstract theorem concerning Cauchy problem solution in a Scale of Banach Spaces. Its basis is the concept of quasidifferential operator. The second part is devoted to a strict justification of the shallow water theory in a class of analytical functions. This is approached by means of the abstract theorem on the example of the plane problem for unsteady periodical waves.
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References
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Ovsjannikov, L.V. (1976). Cauchy problem in a scale of banach spaces and its application to the shallow water theory justification. In: Germain, P., Nayroles, B. (eds) Applications of Methods of Functional Analysis to Problems in Mechanics. Lecture Notes in Mathematics, vol 503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088777
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DOI: https://doi.org/10.1007/BFb0088777
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