Logarithmic well-posed approximation of the backward heat equation in Banach space

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Abstract

In this paper, we apply a logarithmic approximation introduced by Boussetila and Rebbani in order to study an ill-posed Cauchy problem in Banach space. The proposed method induces a well-posed problem whose approximation parameter yields continuous dependence on modeling. Throughout, properties of holomorphic semigroups are utilized culminating in the motivating application which is the backward heat equation in L p (R), 1<p<∞.

Original languageEnglish (US)
Pages (from-to)1367-1384
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume475
Issue number2
DOIs
Publication statusPublished - Jul 15 2019

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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