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

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish (US)
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer Science and Business Media Deutschland GmbH
Pages235-253
Number of pages19
DOIs
StatePublished - 2021

Publication series

NameOperator Theory: Advances and Applications
Volume282
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

All Science Journal Classification (ASJC) codes

  • Analysis

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