### Abstract

We present an introduction to the theory of viscosity solutions of first-order partial differential equations and a review on the optimal control/dynamical approach to the large time behavior of solutions of Hamilton-Jacobi equations, with the Neumann boundary condition. This article also includes some of basics of mathematical analysis related to the optimal control/dynamical approach for easy accessibility to the topics.

Original language | English |
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Title of host publication | Lecture Notes in Mathematics |

Pages | 111-249 |

Number of pages | 139 |

Volume | 2074 |

DOIs | |

Publication status | Published - 2013 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 2074 |

ISSN (Print) | 00758434 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Ishii, H. (2013). A short introduction to viscosity solutions and the large time behavior of solutions of Hamilton-Jacobi equations. In

*Lecture Notes in Mathematics*(Vol. 2074, pp. 111-249). (Lecture Notes in Mathematics; Vol. 2074). https://doi.org/10.1007/978-3-642-36433-4-3