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

Research output: Contribution to journalArticle

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
StatePublished - Jul 15 2019

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Banach spaces
Heat Equation
Logarithmic
Banach space
Holomorphic Semigroups
Well-posed Problem
Continuous Dependence
Ill-posed Problem
Approximation
Cauchy Problem
Modeling
Hot Temperature

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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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<∞.",
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Logarithmic well-posed approximation of the backward heat equation in Banach space. / Fury, Matthew Alexander.

In: Journal of Mathematical Analysis and Applications, Vol. 475, No. 2, 15.07.2019, p. 1367-1384.

Research output: Contribution to journalArticle

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