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Integrated Semigroups and Cauchy Problems with Non-dense Domain

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Theory and Applications of Abstract Semilinear Cauchy Problems

Part of the book series: Applied Mathematical Sciences ((AMS,volume 201))

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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.

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Authors and Affiliations

  1. Institut de Mathématiques de Bordeaux, Université de Bordeaux, Talence, France

    Pierre Magal

  2. Department of Mathematics, University of Miami, Coral Gables, FL, USA

    Shigui Ruan

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  1. Pierre Magal
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  2. Shigui Ruan
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Magal, P., Ruan, S. (2018). Integrated Semigroups and Cauchy Problems with Non-dense Domain. In: Theory and Applications of Abstract Semilinear Cauchy Problems. Applied Mathematical Sciences, vol 201. Springer, Cham. https://doi.org/10.1007/978-3-030-01506-0_3

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