Pseudo-analysis approach to nonlinear partial differential equations

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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 languageEnglish
JournalActa Polytechnica Hungarica
Volume5
Issue number1
Publication statusPublished - 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)

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