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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

There is given an overview of methods of pseudoanalysis 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.

Original languageEnglish
Title of host publication5th International Symposium on Intelligent Systems and Informatics, SISY 2007
Pages7-12
Number of pages6
DOIs
Publication statusPublished - 2007
Event5th International Symposium on Intelligent Systems and Informatics, SISY 2007 - Subotica, Serbia
Duration: Aug 24 2007Aug 25 2007

Other

Other5th International Symposium on Intelligent Systems and Informatics, SISY 2007
CountrySerbia
CitySubotica
Period8/24/078/25/07

Fingerprint

Nonlinear equations
Partial differential equations
Hamiltonians
Fluid mechanics
Linear equations
Control theory
Convolution
Image processing
Costs
Nonlinear partial differential equations

ASJC Scopus subject areas

  • Artificial Intelligence
  • Information Systems
  • Information Systems and Management
  • Control and Systems Engineering

Cite this

Pap, E. (2007). Applications of pseudo-analysis on models with nonlinear partial differential equations. In 5th International Symposium on Intelligent Systems and Informatics, SISY 2007 (pp. 7-12). [4342614] https://doi.org/10.1109/SISY.2007.4342614

Applications of pseudo-analysis on models with nonlinear partial differential equations. / Pap, E.

5th International Symposium on Intelligent Systems and Informatics, SISY 2007. 2007. p. 7-12 4342614.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Pap, E 2007, Applications of pseudo-analysis on models with nonlinear partial differential equations. in 5th International Symposium on Intelligent Systems and Informatics, SISY 2007., 4342614, pp. 7-12, 5th International Symposium on Intelligent Systems and Informatics, SISY 2007, Subotica, Serbia, 8/24/07. https://doi.org/10.1109/SISY.2007.4342614
Pap E. Applications of pseudo-analysis on models with nonlinear partial differential equations. In 5th International Symposium on Intelligent Systems and Informatics, SISY 2007. 2007. p. 7-12. 4342614 https://doi.org/10.1109/SISY.2007.4342614
Pap, E. / Applications of pseudo-analysis on models with nonlinear partial differential equations. 5th International Symposium on Intelligent Systems and Informatics, SISY 2007. 2007. pp. 7-12
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