Solutions of Smooth Nonlinear Partial Differential Equations
Author
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-37, 37 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-06-30
Country of Publication
Egypt
No. of Pages
37
Main Subjects
Abstract EN
The method of order completion provides a general and type-independent theory for the existence and basic regularity of the solutions of large classes of systems of nonlinear partial differential equations (PDEs).
Recently, the application of convergence spaces to this theory resulted in a significant improvement upon the regularity of the solutions and provided new insight into the structure of solutions.
In this paper, we show how this method may be adapted so as to allow for the infinite differentiability of generalized functions.
Moreover, it is shown that a large class of smooth nonlinear PDEs admit generalized solutions in the space constructed here.
As an indication of how the general theory can be applied to particular nonlinear equations, we construct generalized solutions of the parametrically driven, damped nonlinear Schrödinger equation in one spatial dimension.
American Psychological Association (APA)
van der Walt, Jan Harm. 2011. Solutions of Smooth Nonlinear Partial Differential Equations. Abstract and Applied Analysis،Vol. 2011, no. 2011, pp.1-37.
https://search.emarefa.net/detail/BIM-488946
Modern Language Association (MLA)
van der Walt, Jan Harm. Solutions of Smooth Nonlinear Partial Differential Equations. Abstract and Applied Analysis No. 2011 (2011), pp.1-37.
https://search.emarefa.net/detail/BIM-488946
American Medical Association (AMA)
van der Walt, Jan Harm. Solutions of Smooth Nonlinear Partial Differential Equations. Abstract and Applied Analysis. 2011. Vol. 2011, no. 2011, pp.1-37.
https://search.emarefa.net/detail/BIM-488946
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-488946