Abstract
The concept of quasidifferential operator in a scale of Banach spaces is formulated. A theorem of existence and uniqueness of a solution to the Cauchy problem for the equation with a nonlinear quasidifferential operator is proved. As an example of application of the theorem, the correctness of the nonlinear nonlocal problem of plane-parallel unsteady potential motion of a liquid with free boundary is proved.
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Vol. 281, pp. 7–15.
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Ovsyannikov, L.V. Cauchy problem in a scale of Banach spaces. Proc. Steklov Inst. Math. 281, 3–11 (2013). https://doi.org/10.1134/S0081543813040020
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DOI: https://doi.org/10.1134/S0081543813040020