Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations

Juraj Húska; Peter Poláčik; Mikhail V. Safonov

doi:10.1016/j.anihpc.2006.04.006

Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations

Juraj Húska, Peter Poláčik, Mikhail V. Safonov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

We consider the Dirichlet problem for linear nonautonomous second order parabolic equations with bounded measurable coefficients on bounded Lipschitz domains. Using a new Harnack-type inequality for quotients of positive solutions, we show that each positive solution exponentially dominates any solution which changes sign for all times. We then examine continuity and robustness properties of a principal Floquet bundle and the associated exponential separation under perturbations of the coefficients and the spatial domain.

Original language	English (US)
Pages (from-to)	711-739
Number of pages	29
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	24
Issue number	5
DOIs	https://doi.org/10.1016/j.anihpc.2006.04.006
State	Published - 2007

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: [email protected] (J. Húska), [email protected] (P. Polácˇik), [email protected] (M.V. Safonov). 1 Supported in part by NSF Grant DMS-0400702.

Keywords

Exponential separation
Harnack inequalities
Perturbations
Positive entire solutions
Principal Floquet bundle
Robustness

Publisher link

10.1016/j.anihpc.2006.04.006

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title = "Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations",

abstract = "We consider the Dirichlet problem for linear nonautonomous second order parabolic equations with bounded measurable coefficients on bounded Lipschitz domains. Using a new Harnack-type inequality for quotients of positive solutions, we show that each positive solution exponentially dominates any solution which changes sign for all times. We then examine continuity and robustness properties of a principal Floquet bundle and the associated exponential separation under perturbations of the coefficients and the spatial domain.",

keywords = "Exponential separation, Harnack inequalities, Perturbations, Positive entire solutions, Principal Floquet bundle, Robustness",

author = "Juraj H{\'u}ska and Peter Pol{\'a}{\v c}ik and Safonov, {Mikhail V.}",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (J. H{\'u}ska), [email protected] (P. Pol{\'a}cˇik), [email protected] (M.V. Safonov). 1 Supported in part by NSF Grant DMS-0400702.",

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doi = "10.1016/j.anihpc.2006.04.006",

language = "English (US)",

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pages = "711--739",

journal = "Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire",

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T1 - Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations

AU - Húska, Juraj

AU - Poláčik, Peter

AU - Safonov, Mikhail V.

N1 - Funding Information: * Corresponding author. E-mail addresses: [email protected] (J. Húska), [email protected] (P. Polácˇik), [email protected] (M.V. Safonov). 1 Supported in part by NSF Grant DMS-0400702.

PY - 2007

Y1 - 2007

N2 - We consider the Dirichlet problem for linear nonautonomous second order parabolic equations with bounded measurable coefficients on bounded Lipschitz domains. Using a new Harnack-type inequality for quotients of positive solutions, we show that each positive solution exponentially dominates any solution which changes sign for all times. We then examine continuity and robustness properties of a principal Floquet bundle and the associated exponential separation under perturbations of the coefficients and the spatial domain.

AB - We consider the Dirichlet problem for linear nonautonomous second order parabolic equations with bounded measurable coefficients on bounded Lipschitz domains. Using a new Harnack-type inequality for quotients of positive solutions, we show that each positive solution exponentially dominates any solution which changes sign for all times. We then examine continuity and robustness properties of a principal Floquet bundle and the associated exponential separation under perturbations of the coefficients and the spatial domain.

KW - Exponential separation

KW - Harnack inequalities

KW - Perturbations

KW - Positive entire solutions

KW - Principal Floquet bundle

KW - Robustness

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DO - 10.1016/j.anihpc.2006.04.006

M3 - Article

AN - SCOPUS:34547575964

SN - 0294-1449

VL - 24

SP - 711

EP - 739

JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 5

ER -

Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations

Abstract

Bibliographical note

Keywords

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