A Cauchy-Kowalevsky Theorem for Overdetermined Systems of Nonlinear Partial Differential Equations and Geometric Applications

被引：1

作者：

Baouendi, M. S. ^{[1
]}

Ebenfelt, P. ^{[1
]}

Zaitsev, D. ^{[2
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Trinity Coll Dublin, Sch Math, Dublin, Ireland

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 34卷 / 10期

基金：

爱尔兰科学基金会;

关键词：

Approximate solutions; Cauchy problem; Exterior differential systems; Finitely nondegenerate hypersurfaces; Levi number; Overdetermined systems; CR-MANIFOLDS; REAL;

D O I：

10.1080/03605300902910220

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a Cauchy problem for an overdetermined system of nonlinear partial differential equations, and give necessary and sufficient conditions for solvability of this Cauchy problem for all data. As an application, we find all real tube hypersurfaces in complex space whose Levi number is maximal.

引用

页码：1180 / 1207

页数：28

共 50 条

[21] Cauchy problem for nonlinear fractional differential equations with positive constant coefficient
Peng S.
Wang J.
J. Appl. Math. Comp., 1-2 (341-351): : 341 - 351
[22] Well-posedness of the cauchy problem for nonlinear differential equations with variable delays
Kharatishvili, GL
Tadumadze, TA
DIFFERENTIAL EQUATIONS, 2004, 40 (03) : 360 - 369
[23] Branching Solutions of the Cauchy Problem for Nonlinear Loaded Differential Equations with Bifurcation Parameters
Sidorov, Nikolai
Sidorov, Denis
MATHEMATICS, 2022, 10 (12)
[24] Well-Posedness of the Cauchy Problem for Nonlinear Differential Equations with Variable Delays
G. L. Kharatishvili
T. A. Tadumadze
Differential Equations, 2004, 40 : 360 - 369
[25] ON THE SOLVABILITY OF THE CAUCHY PROBLEM FOR SYSTEMS OF TWO LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS
Bravyi, E. I.
MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2007, 41 : 11 - 26
[26] SOLVING A FEW LINEAR PARTIAL DIFFERENTIAL EQUATIONS (PDEs) OF CAUCHY KIND BY THE SBA METHOD
Youssouf, Minoungou
Moussa, Bagayogo
Pare, Youssouf
Some, Blaise
ADVANCES IN DIFFERENTIAL EQUATIONS AND CONTROL PROCESSES, 2019, 20 (01): : 115 - 128
[27] GEVREY REGULARITY OF THE SOLUTIONS OF INHOMOGENEOUS NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
Remy, Pascal
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 2023 (06) : 1 - 28
[28] On the Fuzzy Solution of Linear-Nonlinear Partial Differential Equations
Osman, Mawia
Xia, Yonghui
Omer, Omer Abdalrhman
Hamoud, Ahmed
MATHEMATICS, 2022, 10 (13)
[29] Some Theorems on Cauchy Problem for Nonlinear Fractional Differential Equations with Positive Constant Coefficient
Shivaji Tate
H. T. Dinde
Mediterranean Journal of Mathematics, 2017, 14
[30] Some Theorems on Cauchy Problem for Nonlinear Fractional Differential Equations with Positive Constant Coefficient
Tate, Shivaji
Dinde, H. T.
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2017, 14 (02)

← 1 2 3 4 5 →