NDLI: Applications of pseudo-analysis on models with nonlinear partial differential equations

Content Provider	IEEE Xplore Digital Library
Author	Pap, E.
Copyright Year	2007
Description	Author affiliation: Univ. of Novi Sad, Novi Sad (Pap, E.)
Abstract	There is given an overview of methods of pseudo-analysis in applications on important classes of nonlinear partial differential equations occurring in different fields, see [7], [8], [12], [16], [18], [19], [20], [21], [22], [24]. Some obtained principles, e. g., the pseudo-linear superposition principle, allows us to transfer the methods of linear equations to the nonlinear equations. Hamilton-Jacobi equations are specially important in the control theory. Unfortunately, usually the interesting models are represented by Hamilton-Jacobi equations in which the nonlinear Hamiltonian H is not smooth, e.g., the absolute value, min or max operations, where it can not apply on such cases the classical mathematical analysis. Using the pseudo-analysis with generalized pseudo-convolution it is possible to obtain solutions which can be interpreted in the mentioned classical way. Another important class of nonlinear equations, where it is applied the pseudo-analysis, are the Burgers type equations and Black and Shole equation in option pricing. Very recent applications of pseudo-analysis are obtained on equations which model fluid mechanics and image processing.
Starting Page	7
Ending Page	12
File Size	748349
Page Count	6
File Format	PDF
ISBN	9781424414420
DOI	10.1109/SISY.2007.4342614
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-08-24
Publisher Place	Serbia
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Nonlinear equations Partial differential equations Mathematical analysis Pricing Mathematics Image restoration Control theory Mathematical model Informatics Intelligent systems
Content Type	Text
Resource Type	Article

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