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

共 50 条

[31] Nonlocal Cauchy problem for analytic resolvent integrodifferential equations in Banach spaces
Kumar, R. Ravi
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 204 (01) : 352 - 362
[32] Convergence of a semi-discrete finite difference scheme applied to the abstract Cauchy problem on a scale of Banach spaces
Iso, Yuusuke
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2011, 87 (07) : 109 - 113
[33] Sobolev's problem in complete scale of Banach spaces
Roitberg, Y
Los, V
Sklyarets, A
[J]. DIFFERENTIAL OPERATORS AND RELATED TOPICS, 2000, 117 : 301 - 312
[34] Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces
Asadollah Aghajani
Ehsan Pourhadi
Juan J. Trujillo
[J]. Fractional Calculus and Applied Analysis, 2013, 16 : 962 - 977
[35] Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces
Aghajani, Asadollah
Pourhadi, Ehsan
Trujillo, Juan J.
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2013, 16 (04) : 962 - 977
[36] ON THE CAUCHY-PROBLEM FOR ORDINARY DIFFERENTIAL-EQUATIONS IN BANACH-SPACES
MONCH, H
VONHARTEN, GF
[J]. ARCHIV DER MATHEMATIK, 1982, 39 (02) : 153 - 160
[37] Nonlocal Cauchy problem for delay integrodifferential equations of Sobolev type in Banach spaces
Balachandran, K
Park, JY
Chandrasekaran, M
[J]. APPLIED MATHEMATICS LETTERS, 2002, 15 (07) : 845 - 854
[38] Nonlocal cauchy problem for second order integrodifferential evolution equations in banach spaces
Balachandran, K.
Kim, J. -H.
[J]. TAIWANESE JOURNAL OF MATHEMATICS, 2007, 11 (05): : 1343 - 1357
[39] Atomic Solution of Fractional Abstract Cauchy Problem of High Order in Banach Spaces
Bekraoui, Fatema
Al Horani, Mohammad
Khalil, Roshdi
[J]. EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2022, 15 (01): : 106 - 125
[40] A positive point of using fixed point theory in K-normed space for Cauchy problem in a scale of Banach spaces
Vo Viet Tri
[J]. JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2022, 25 (01) : 155 - 162

← 1 2 3 4 5 →