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Integrated Semigroups and Cauchy Problems with Non-dense Domain
Book chapter

Integrated Semigroups and Cauchy Problems with Non-dense Domain

Pierre Magal and Shigui Ruan
Theory and Applications of Abstract Semilinear Cauchy Problems, pp.101-164
Applied Mathematical Sciences, Springer International Publishing
2018-11-22
DOI: https://doi.org/10.1007/978-3-030-01506-0_3

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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