### Abstract

An overview of methods of pseudo-analysis in applications on important classes of nonlinear partial differential equations, occurring in different fields, is given. Hamilton-Jacobi equations, specially important in the control theory, are for impor- tant models usually with non-linear Hamiltonian H which is also not smooth, e.g., the absolute value, min or max operations, where it can not apply the classical math- ematical 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 classes of nonlinear equations, where there are applied the pseudo-analysis, are the Burgers type equations and Black and Shole equation in op- tion pricing. Very recent applications of pseudo-analysis are obtained on equations which model fluid mechanics (Navier-Stokes equation) and image processing (Perona and Malik equation).

Original language | English |
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Journal | Acta Polytechnica Hungarica |

Volume | 5 |

Issue number | 1 |

Publication status | Published - Dec 1 2008 |

### Keywords

- Bellman differential equation
- Burgers type equation
- Hamilton-Jacobi equation
- Navier-Stokes equation
- Nonlinear partial differential equation
- Perona and Malik equation
- Pseudo-analysis

### ASJC Scopus subject areas

- Engineering(all)