### 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 language | English |
---|---|

Title of host publication | 5th International Symposium on Intelligent Systems and Informatics, SISY 2007 |

Pages | 7-12 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2007 |

Event | 5th International Symposium on Intelligent Systems and Informatics, SISY 2007 - Subotica, Serbia Duration: Aug 24 2007 → Aug 25 2007 |

### Other

Other | 5th International Symposium on Intelligent Systems and Informatics, SISY 2007 |
---|---|

Country | Serbia |

City | Subotica |

Period | 8/24/07 → 8/25/07 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Applications of pseudo-analysis on models with nonlinear partial differential equations

AU - Pap, E.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=48049098381&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=48049098381&partnerID=8YFLogxK

U2 - 10.1109/SISY.2007.4342614

DO - 10.1109/SISY.2007.4342614

M3 - Conference contribution

AN - SCOPUS:48049098381

SN - 1424414431

SN - 9781424414437

SP - 7

EP - 12

BT - 5th International Symposium on Intelligent Systems and Informatics, SISY 2007

ER -