Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

6 Issues per year


IMPACT FACTOR 2017: 0.314
5-year IMPACT FACTOR: 0.462

CiteScore 2017: 0.46

SCImago Journal Rank (SJR) 2017: 0.339
Source Normalized Impact per Paper (SNIP) 2017: 0.845

Mathematical Citation Quotient (MCQ) 2017: 0.26

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 68, Issue 5

Issues

Approximate sentinels for diffusion phenomena with pollution

Fouzia Segueni / Mohammed Hichem Mortad / Abdennebi Omrane
Published Online: 2018-10-20 | DOI: https://doi.org/10.1515/ms-2017-0168

Abstract

Modeling ecological and environmental problems lead to the study of mathematical systems with missing data. In this paper we study a parameter identification question of a pollution problem using the method of sentinels by Lions (1992). Our system, which is a spatio-temporal one contains a missing initial condition.

We show that the question of existence of a sentinel insensitive to the initial condition is equivalent to an approximate null-controllability problem for which we present a variational method.

MSC 2010: 35B37; 35K55; 90C30; 93A15

Keywords: spatio-temporal systems; pollution; approximate sentinels; approximate null-controllability; variational method

References

  • [1]

    AINSEBA, B.-E.—KERNEVEZ, J.-P.—LUCE, R.: Application des sentinelles à l’identification des pollutions dans une rivière, Math. Model. Numer. Anal. (M2AN) 28(3) (1994), 297–312.Google Scholar

  • [2]

    BODART, O.—FABRE, C.: Contrôle insensibilisant la norme de la solution d’une équation de la chaleur semi-linéaire, C.R. Acad. Sci., Série I 316(8), (1993), 789–794.Google Scholar

  • [3]

    KERNEVEZ, J.-P.: The Sentinel Method and Its Application to Environmental Pollution Problems, CRC Press, 1997.Google Scholar

  • [4]

    LEBLOND, J.—MARMORAT, J.-P.—PARTINGTON, J. R.: Analytic approximation with real constraints with applications to inverse diffusion problems, J. Inverse Ill-Posed Probl. 16 (2008), 89–105.Google Scholar

  • [5]

    LIONS, J.-L.: Sentinelles pour les Systèmes Distribués à Données Incomplètes. Recherches en Mathématiques Appliquées (RMA) 21, Masson, 1992.Google Scholar

  • [6]

    LIONS, J.-L.—MAGENES, E.: Problèmes aux Limites non Homogènes et Applications, Vol. 1 & 2, Masson, 1970.Google Scholar

  • [7]

    MIZOHATA, Z.: Unicité du prolongement des solutions pour quelques opérateurs différentiels paraboliques, Mem. Coll. Sc. Univ. Kyoto, Série A 31 (1958), 219–239.Google Scholar

  • [8]

    OMRANE, A.: Some aspects of the sentinel method for pollution problems. In: Air Quality - Monitoring and Modeling, Chap 9, In TechOpen, 2012, pp. 185–204. DOI. 10.5772/33173Google Scholar

  • [9]

    ZUAZUA, E.: Finite dimensional null-controllability for the semilinear heat equation, J. Math. Pures Appl. 76 (1997), 570–594.Google Scholar

About the article

Received: 2017-05-14

Accepted: 2017-09-21

Published Online: 2018-10-20

Published in Print: 2018-10-25


Communicated by Sylvia Pulmannová


Citation Information: Mathematica Slovaca, Volume 68, Issue 5, Pages 1065–1074, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0168.

Export Citation

© 2018 Mathematical Institute Slovak Academy of Sciences.Get Permission

Comments (0)

Please log in or register to comment.
Log in