### 抄録

The existence, uniqueness and regularity of strong solutions for Cauchy problem and periodic problem are studied for the evolution equation: du(t)/dt + ∂φ(u(t)) ∋ f(t), t ∈]0, T[, where ∂φ is the so-called subdifferential operator from a real Banach space V into its dual V*. The study in the Hilbert space setting (V = V* = H: Hilbert space) is already developed in detail so far. However, the study here is done in the V-V* setting which is not yet fully pursued. Our method of proof relies on approximation arguments in a Hilbert space H. To assure this procedure, it is assumed that the embeddings V ⊂ H ⊂ V* are both dense and continuous.

元の言語 | English |
---|---|

ページ（範囲） | 519-541 |

ページ数 | 23 |

ジャーナル | Journal of Evolution Equations |

巻 | 4 |

発行部数 | 4 |

DOI | |

出版物ステータス | Published - 2004 12 |

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### ASJC Scopus subject areas

- Ecology, Evolution, Behavior and Systematics

### これを引用

**Evolution inclusions governed by subdifferentials in reflexive Banach spaces.** / Akagi, Goro; Otani, Mitsuharu.

研究成果: Article

*Journal of Evolution Equations*, 巻. 4, 番号 4, pp. 519-541. https://doi.org/10.1007/s00028-004-0162-y

}

TY - JOUR

T1 - Evolution inclusions governed by subdifferentials in reflexive Banach spaces

AU - Akagi, Goro

AU - Otani, Mitsuharu

PY - 2004/12

Y1 - 2004/12

N2 - The existence, uniqueness and regularity of strong solutions for Cauchy problem and periodic problem are studied for the evolution equation: du(t)/dt + ∂φ(u(t)) ∋ f(t), t ∈]0, T[, where ∂φ is the so-called subdifferential operator from a real Banach space V into its dual V*. The study in the Hilbert space setting (V = V* = H: Hilbert space) is already developed in detail so far. However, the study here is done in the V-V* setting which is not yet fully pursued. Our method of proof relies on approximation arguments in a Hilbert space H. To assure this procedure, it is assumed that the embeddings V ⊂ H ⊂ V* are both dense and continuous.

AB - The existence, uniqueness and regularity of strong solutions for Cauchy problem and periodic problem are studied for the evolution equation: du(t)/dt + ∂φ(u(t)) ∋ f(t), t ∈]0, T[, where ∂φ is the so-called subdifferential operator from a real Banach space V into its dual V*. The study in the Hilbert space setting (V = V* = H: Hilbert space) is already developed in detail so far. However, the study here is done in the V-V* setting which is not yet fully pursued. Our method of proof relies on approximation arguments in a Hilbert space H. To assure this procedure, it is assumed that the embeddings V ⊂ H ⊂ V* are both dense and continuous.

KW - Evolution equation

KW - Reflexive Banach space

KW - Subdifferential

UR - http://www.scopus.com/inward/record.url?scp=12444264963&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12444264963&partnerID=8YFLogxK

U2 - 10.1007/s00028-004-0162-y

DO - 10.1007/s00028-004-0162-y

M3 - Article

AN - SCOPUS:12444264963

VL - 4

SP - 519

EP - 541

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

SN - 1424-3199

IS - 4

ER -