### Abstract

This article presents a theorem for guaranteeing existence of a solution for an initial-boundary value problem of semilinear parabolic equations. The sufficient condition of our main theorem is derived by a fixed-point formulation using the evolution operator. We note that the sufficient condition can be checked by verified numerical computations.

Original language | English |
---|---|

Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 218-223 |

Number of pages | 6 |

Volume | 9582 |

ISBN (Print) | 9783319328584 |

DOIs | |

Publication status | Published - 2016 |

Event | 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015 - Berlin, Germany Duration: 2015 Nov 11 → 2015 Nov 13 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 9582 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015 |
---|---|

Country | Germany |

City | Berlin |

Period | 15/11/11 → 15/11/13 |

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

## Fingerprint Dive into the research topics of 'Verified computations for solutions to semilinear parabolic equations using the evolution operator'. Together they form a unique fingerprint.

## Cite this

Takayasu, A., Mizuguchi, M., Kubo, T., & Oishi, S. (2016). Verified computations for solutions to semilinear parabolic equations using the evolution operator. In

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 9582, pp. 218-223). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9582). Springer Verlag. https://doi.org/10.1007/978-3-319-32859-1_18