### 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 |
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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) |
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Volume | 9582 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

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

City | Berlin |

Period | 15/11/11 → 15/11/13 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*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

**Verified computations for solutions to semilinear parabolic equations using the evolution operator.** / Takayasu, Akitoshi; Mizuguchi, Makoto; Kubo, Takayuki; Oishi, Shinichi.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 9582, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9582, Springer Verlag, pp. 218-223, 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015, Berlin, Germany, 15/11/11. https://doi.org/10.1007/978-3-319-32859-1_18

}

TY - GEN

T1 - Verified computations for solutions to semilinear parabolic equations using the evolution operator

AU - Takayasu, Akitoshi

AU - Mizuguchi, Makoto

AU - Kubo, Takayuki

AU - Oishi, Shinichi

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84964047111&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964047111&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-32859-1_18

DO - 10.1007/978-3-319-32859-1_18

M3 - Conference contribution

AN - SCOPUS:84964047111

SN - 9783319328584

VL - 9582

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 218

EP - 223

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

PB - Springer Verlag

ER -