@inbook{6d8131bc15334225adc2a2b117895485,

title = "Convergence Rates for Solutions of Inhomogeneous Ill-posed Problems in Banach Space with Sufficiently Smooth Data",

abstract = "We consider the inhomogeneous, ill-posed Cauchy problem (formula presented) where A is the infinitesimal generator of a holomorphic semigroup of angle θ in Banach space. As in conventional regularization methods, certain auxiliary well-posed problems and their associated C0 semigroups are applied in order to approximate a known solution u. A key property however, that the semigroups adhere to requisite growth orders, may fail depending on the value of the angle Our results show that an approximation of u may be still be established in such situations as long as the data of the original problem is sufficiently smooth, i.e. in a small enough domain. Our results include well-known examples applied in the approach of quasi-reversibility as well as other types of approximations. The outcomes of the paper may be applied to partial differential equations in Lp spaces, 1 < p < defined by strongly elliptic differential operators.",

author = "Fury, {Matthew A.}",

note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.",

year = "2021",

doi = "10.1007/978-3-030-51945-2_12",

language = "English (US)",

series = "Operator Theory: Advances and Applications",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "235--253",

booktitle = "Operator Theory",

address = "Germany",

}