### 抄録

This paper considers a backward problem on a heat equation with a fractional Laplacian. It is not easy to solve a backward heat equation directly. This problem is a well-known ill-posed problem. In order to consider a backward heat equation with a fractional Laplacian, we apply the N-th power of the Dirichlet-Laplacian and small parameters to regularize the equation. This method is called a quasi-reversibility method. We use the generalized quasi-reversibility method to change the backward heat system into another system. This paper shows the existence of a strong solution of the modified backward heat system, and derives L^{2}-estimates of the difference between a solution of the heat equation with the fractional Laplacian and a solution of our system.

元の言語 | English |
---|---|

ページ（範囲） | 47-57 |

ページ数 | 11 |

ジャーナル | Analysis |

巻 | 35 |

発行部数 | 1 |

DOI | |

出版物ステータス | Published - 2015 3 1 |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics
- Analysis
- Numerical Analysis

### これを引用

*Analysis*,

*35*(1), 47-57. https://doi.org/10.1515/anly-2014-1262

**Generalized quasi-reversibility method for a backward heat equation with a fractional Laplacian.** / Koba, Hajime; Matsuoka, Hideki.

研究成果: Article

*Analysis*, 巻. 35, 番号 1, pp. 47-57. https://doi.org/10.1515/anly-2014-1262

}

TY - JOUR

T1 - Generalized quasi-reversibility method for a backward heat equation with a fractional Laplacian

AU - Koba, Hajime

AU - Matsuoka, Hideki

PY - 2015/3/1

Y1 - 2015/3/1

N2 - This paper considers a backward problem on a heat equation with a fractional Laplacian. It is not easy to solve a backward heat equation directly. This problem is a well-known ill-posed problem. In order to consider a backward heat equation with a fractional Laplacian, we apply the N-th power of the Dirichlet-Laplacian and small parameters to regularize the equation. This method is called a quasi-reversibility method. We use the generalized quasi-reversibility method to change the backward heat system into another system. This paper shows the existence of a strong solution of the modified backward heat system, and derives L2-estimates of the difference between a solution of the heat equation with the fractional Laplacian and a solution of our system.

AB - This paper considers a backward problem on a heat equation with a fractional Laplacian. It is not easy to solve a backward heat equation directly. This problem is a well-known ill-posed problem. In order to consider a backward heat equation with a fractional Laplacian, we apply the N-th power of the Dirichlet-Laplacian and small parameters to regularize the equation. This method is called a quasi-reversibility method. We use the generalized quasi-reversibility method to change the backward heat system into another system. This paper shows the existence of a strong solution of the modified backward heat system, and derives L2-estimates of the difference between a solution of the heat equation with the fractional Laplacian and a solution of our system.

KW - 35K05

KW - Primary 35R30

KW - secondary 35R25

UR - http://www.scopus.com/inward/record.url?scp=84925450481&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84925450481&partnerID=8YFLogxK

U2 - 10.1515/anly-2014-1262

DO - 10.1515/anly-2014-1262

M3 - Article

AN - SCOPUS:84925450481

VL - 35

SP - 47

EP - 57

JO - Analysis (Germany)

JF - Analysis (Germany)

SN - 0174-4747

IS - 1

ER -