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Journal of Inverse and Ill-posed Problems

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Solving a scalar degenerate multidimensional identification problem in a Banach space

M. Ivanchov1 / A. Lorenzi2 / N. Saldina3

1 Department of Mathematics and Mechanics, Ivan Franko National University of Lviv, Universitetska St. 1, 79000, Lviv, Ukraine. Email:

2 Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy. Email:

3 Department of Mathematics and Mechanics, Ivan Franko National University of Lviv, Universitetska St. 1, 79000, Lviv, Ukraine. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 16, Issue 4, Pages 397–415, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2008.022, September 2008

Publication History

Received:
2007-12-04
Accepted:
2008-02-18
Published Online:
2008-09-11

Abstract

We recover a non-negative time-dependent function, vanishing only at t = 0, in a linear multi-dimensional parabolic equation with a power degeneration. First we prove an existence and uniqueness result for an identification problem in a general Banach space via Semigroup Theory. Then we apply such a result to our specific linear parabolic equation related to a smooth bounded domain in ℝn.

Key words.: Identification problems; linear degenerate parabolic equations; first-order linear differential equations in Banach spaces; Semigroup Theory; existence and uniqueness results

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[1]
Mykola I. Ivanchov and Tetyana Savitska
Journal of Mathematical Sciences, 2012, Volume 181, Number 1, Page 47

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