### Abstract

The goal of this chapter is to introduce the integrated semigroup theory and use it to investigate the existence and uniqueness of integrated (mild) solutions of the nonhomogeneous Cauchy problems when the domain of the linear operator A is not dense in the state space and A is not a Hille-Yosida operator.

Original language | English (US) |
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Title of host publication | Applied Mathematical Sciences (Switzerland) |

Publisher | Springer |

Pages | 101-164 |

Number of pages | 64 |

DOIs | |

State | Published - Jan 1 2018 |

### Publication series

Name | Applied Mathematical Sciences (Switzerland) |
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Volume | 201 |

ISSN (Print) | 0066-5452 |

ISSN (Electronic) | 2196-968X |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Applied Mathematical Sciences (Switzerland)*(pp. 101-164). (Applied Mathematical Sciences (Switzerland); Vol. 201). Springer. https://doi.org/10.1007/978-3-030-01506-0_3

**Integrated Semigroups and Cauchy Problems with Non-dense Domain.** / Magal, Pierre; Ruan, Shigui.

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

*Applied Mathematical Sciences (Switzerland).*Applied Mathematical Sciences (Switzerland), vol. 201, Springer, pp. 101-164. https://doi.org/10.1007/978-3-030-01506-0_3

}

TY - CHAP

T1 - Integrated Semigroups and Cauchy Problems with Non-dense Domain

AU - Magal, Pierre

AU - Ruan, Shigui

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The goal of this chapter is to introduce the integrated semigroup theory and use it to investigate the existence and uniqueness of integrated (mild) solutions of the nonhomogeneous Cauchy problems when the domain of the linear operator A is not dense in the state space and A is not a Hille-Yosida operator.

AB - The goal of this chapter is to introduce the integrated semigroup theory and use it to investigate the existence and uniqueness of integrated (mild) solutions of the nonhomogeneous Cauchy problems when the domain of the linear operator A is not dense in the state space and A is not a Hille-Yosida operator.

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U2 - 10.1007/978-3-030-01506-0_3

DO - 10.1007/978-3-030-01506-0_3

M3 - Chapter

AN - SCOPUS:85068141401

T3 - Applied Mathematical Sciences (Switzerland)

SP - 101

EP - 164

BT - Applied Mathematical Sciences (Switzerland)

PB - Springer

ER -