Cauchy problem in a scale of Banach spaces

被引：6

作者：

Ovsyannikov, L. V. ^{[1
]}

机构：

[1] Russian Acad Sci, MA Lavrentev Hydrodynam Inst, Siberian Branch, Novosibirsk 630090, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2013年 / 281卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

Banach Space; Cauchy Problem; Free Boundary; STEKLOV Institute; Conformal Mapping;

D O I：

10.1134/S0081543813040020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：3 / 11

页数：9

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