Regularization for a class of ill-posed evolution problems in Banach space

Matthew A. Fury, Rhonda J. Hughes

Research output: Contribution to journalArticle

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Abstract

We study evolution equations in Banach space, and provide a general framework for regularizing a wide class of ill-posed Cauchy problems by proving continuous dependence on modeling for nonautonomous equations. We approximate the ill-posed problem by a well-posed one, and obtain Hölder-continuous dependence results that provide estimates of the error for a class of solutions under certain stabilizing conditions. For examples that include the linearized Korteweg-de Vries equation and the Schrödinger equation in L p,p≠2, we obtain a family of regularizing operators for the ill-posed problem. This work extends to the nonautonomous case several recent results for ill-posed problems with constant coefficients.

Original languageEnglish (US)
Pages (from-to)191-212
Number of pages22
JournalSemigroup Forum
Volume85
Issue number2
DOIs
StatePublished - Oct 1 2012

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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