Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0632.35038
Kato, Tosio
On nonlinear Schrödinger equations. (English)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 46, 113-129 (1987). ISSN 0246-0211

The nonlinear Schrödinger equation $iu\sb t=-\Delta u+F(u)$ is considered. \par The author investigates questions concerning the local and global existence, uniqueness, continuous dependence on the initial value and regularity of the solution of the corresponding Cauchy problem. \par The introduction contains a clear and condensed representation of the theorems. Therefore, it gives a good survey on recent results for the initial value problem. As the author remarks, not all results are new. However, all theorems are proved without using growth conditions of F(x) for small x.
[L.Brüll]

MSC 2000:: *35L60 First-order nonlinear hyperbolic equations
35A05 General existence and uniqueness theorems (PDE)
35A07 Local existence and uniqueness theorems (PDE)
35B65 Smoothness of solutions of PDE
35B30 Dependence of solutions of PDE on initial and boundary data

Keywords: nonlinear Schrödinger equation; existence; uniqueness; continuous dependence; regularity; Cauchy problem; survey

Cited in: Zbl 1038.35119 Zbl 0754.76068

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]