A strongly ill-posed integrodifferential singular parabolic problem in the unit cube of $\mathbb{R}^n$

Alfredo Lorenzi; Luca Lorenzi

doi:10.3934/eect.2014.3.499

Article Contents

2014, Volume 3, Issue 3: 499-524. Doi: 10.3934/eect.2014.3.499

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A strongly ill-posed integrodifferential singular parabolic problem in the unit cube of $\mathbb{R}^n$

Alfredo Lorenzi^1, and
Luca Lorenzi^2,

1.
Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano
2.
Dipartimento di Matematica, Università degli Studi di Parma, Viale Parco Area delle Scienze 53/A, I-43124 Parma

Received: March 31, 2013

Revised: April 30, 2014

Published: August 2014

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Abstract

Via Carleman's estimates we prove uniqueness and continuous dependence results for a severely ill-posed linear integro-differential singular parabolic problems without initial conditions.

Keywords:

Ill-posed problems,
linear singular differential and integro-differential parabolic equations,
Carleman estimates,
uniqueness,
continuous dependence results.

Mathematics Subject Classification: Primary: 30R35; Secondary: 35K20, 34G10, 45N05, 45Q05.

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References

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