Study in the Hölder spaces of boundary value and transmission problems in a domain with thin layer.
Identifieur interne : 000586 ( Hal/Checkpoint ); précédent : 000585; suivant : 000587Study in the Hölder spaces of boundary value and transmission problems in a domain with thin layer.
Auteurs : Omar Belhamiti [France]Source :
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Abstract
We consider a family (Pδ)δ>0 of boundary value and transmission problems in a domain with thin layer, written in the form of second order abstract differential equation of elliptic type. A new approach for the resolution of (Pδ)δ>0 is presented in this work using the physical concept of impedance. This method is different of the one performing a rescaling in the thin layer, see [Favini A., Labbas R., Lemrabet K. and Maingot S.]. It leads to obtain direct and simplified problems. Where the thin layer effect is completely described by the impedance operator. The techniques employed are primarily based on the functional calculation of Dunford, the semigroups theory, the interpolation and some ideas of work in [R. Labbas, Thesis], [Dore G., Favini A., Labbas R., Lemrabet K. and Maingot S.] and [Favini A., Labbas R., Maingot S., Tanabe H., Yagi A.]. We obtain existence, uniqueness and maximal regularities new results in the Hölder spaces for the fixed and then we study the limit passage when δ→0 of (Pδ)δ>0. This work complete thus what was obtained in the framework Lp, see [Favini A., Labbas R., Lemrabet K. and Maingot S.].
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A new approach for the resolution of (Pδ)δ>0 is presented in this work using the physical concept of impedance. This method is different of the one performing a rescaling in the thin layer, see [Favini A., Labbas R., Lemrabet K. and Maingot S.]. It leads to obtain direct and simplified problems. Where the thin layer effect is completely described by the impedance operator. The techniques employed are primarily based on the functional calculation of Dunford, the semigroups theory, the interpolation and some ideas of work in [R. Labbas, Thesis], [Dore G., Favini A., Labbas R., Lemrabet K. and Maingot S.] and [Favini A., Labbas R., Maingot S., Tanabe H., Yagi A.]. We obtain existence, uniqueness and maximal regularities new results in the Hölder spaces for the fixed and then we study the limit passage when δ→0 of (Pδ)δ>0. This work complete thus what was obtained in the framework Lp, see [Favini A., Labbas R., Lemrabet K. and Maingot S.].</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Study in the Hölder spaces of boundary value and transmission problems in a domain with thin layer.</title><title xml:lang="fr">Étude dans les espaces de Hölder de problèmes aux limites et de transmission dans un domaine avec couche mince.</title><author role="aut"><persName><forename type="first">Omar</forename><surname>Belhamiti</surname></persName><email>belhamitio@yahoo.fr</email><idno type="halauthor">360705</idno><affiliation ref="#struct-87"></affiliation></author><editor role="depositor"><persName><forename>Omar</forename><surname>Belhamiti</surname></persName><email>belhamitio@yahoo.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2008-10-15 12:37:54</date><date type="whenModified">2008-10-15 13:15:37</date><date type="whenReleased">2008-10-15 13:15:37</date><date type="whenProduced">2008-05-26</date><date type="whenEndEmbargoed">2008-10-15</date><ref type="file" target="https://tel.archives-ouvertes.fr/tel-00330880/document"><date notBefore="2008-10-15"></date></ref><ref type="file" n="1" target="https://tel.archives-ouvertes.fr/tel-00330880/file/TheseBelhamitiOmar.pdf"><date notBefore="2008-10-15"></date></ref></edition><respStmt><resp>contributor</resp><name key="132372"><persName><forename>Omar</forename><surname>Belhamiti</surname></persName><email>belhamitio@yahoo.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">tel-00330880</idno><idno type="halUri">https://tel.archives-ouvertes.fr/tel-00330880</idno><idno type="halBibtex">belhamiti:tel-00330880</idno><idno type="halRefHtml">Mathématiques [math]. Université du Havre, 2008. Français</idno><idno type="halRef">Mathématiques [math]. Université du Havre, 2008. Français</idno></publicationStmt><seriesStmt><idno type="stamp" n="UNIV-LEHAVRE">Université du Havre</idno><idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno></seriesStmt><notesStmt></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Study in the Hölder spaces of boundary value and transmission problems in a domain with thin layer.</title><title xml:lang="fr">Étude dans les espaces de Hölder de problèmes aux limites et de transmission dans un domaine avec couche mince.</title><author role="aut"><persName><forename type="first">Omar</forename><surname>Belhamiti</surname></persName><email>belhamitio@yahoo.fr</email><idno type="halAuthorId">360705</idno><affiliation ref="#struct-87"></affiliation></author></analytic><monogr><imprint><date type="dateDefended">2008-05-26</date></imprint><authority type="institution">Université du Havre</authority><authority type="supervisor">M. Rabah Labbas (Université du Havre) et M. Ahmed Medeghri (Université de Mostaganem)(rabah.labbas@univ-lehavre.fr et medeghri@univ-mosta.dz)</authority><authority type="jury">M. M. MOUSSAOUI, Professeur, Ecole Centrale de Lyon (Rapporteur).</authority><authority type="jury">M. K. LEMRABET, Professeur, USTHB Alger (Algérie)(Rapporteur).</authority><authority type="jury">M. B. BELAIDI , Professeur, Université de Mostaganem (Algérie)(Président).</authority><authority type="jury">M. S. MAINGOT, Maître de Conférences, Université du Havre (Examinateur).</authority><authority type="jury">M. A. AIBECHE, Professeur, Université de Sétif (Algérie)(Examinateur).</authority><authority type="jury">M. M. AZIZ ALAOUI, Professeur, Université du Havre (Examinateur).</authority></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="fr">French</language></langUsage><textClass><keywords scheme="author"><term xml:lang="en">Abstract differential equation of elliptic type</term><term xml:lang="en">Transmission problems</term><term xml:lang="en">Hölder spaces</term><term xml:lang="en">semigroups</term><term xml:lang="en">fractional powers of operator</term><term xml:lang="en">Dunford operational calculus.</term><term xml:lang="fr">calcul fonctionnel de Dunford</term><term xml:lang="fr">Équations différentielles abstraites de type elliptique</term><term xml:lang="fr">problèmes de transmission</term><term xml:lang="fr">espaces de Hölder</term><term xml:lang="fr">interpolation</term><term xml:lang="fr">semi-groupes</term><term xml:lang="fr">puissances fractionnaires d'opérateur</term><term xml:lang="fr">calcul fonctionnel de Dunford.</term></keywords><classCode scheme="halDomain" n="math">Mathematics [math]</classCode><classCode scheme="halTypology" n="THESE">Theses</classCode></textClass><abstract xml:lang="en">We consider a family (Pδ)δ>0 of boundary value and transmission problems in a domain with thin layer, written in the form of second order abstract differential equation of elliptic type. A new approach for the resolution of (Pδ)δ>0 is presented in this work using the physical concept of impedance. This method is different of the one performing a rescaling in the thin layer, see [Favini A., Labbas R., Lemrabet K. and Maingot S.]. It leads to obtain direct and simplified problems. Where the thin layer effect is completely described by the impedance operator. The techniques employed are primarily based on the functional calculation of Dunford, the semigroups theory, the interpolation and some ideas of work in [R. Labbas, Thesis], [Dore G., Favini A., Labbas R., Lemrabet K. and Maingot S.] and [Favini A., Labbas R., Maingot S., Tanabe H., Yagi A.]. We obtain existence, uniqueness and maximal regularities new results in the Hölder spaces for the fixed and then we study the limit passage when δ→0 of (Pδ)δ>0. This work complete thus what was obtained in the framework Lp, see [Favini A., Labbas R., Lemrabet K. and Maingot S.].</abstract><abstract xml:lang="fr">On considère une famille (Pδ)δ>0 de problèmes aux limites et de transmission dans un domaine avec couche mince, écrit sous la forme d'une équation différentielle d'ordre deux abstraite de type elliptique . Une nouvelle approche pour la résolution de (Pδ)δ>0 est présentée dans ce travail utilisant le concept physique d'impédance. Cette méthode est différente de celle qui utilise un changement d'échelle sur la couche mince voir [Favini A., Labbas R., Lemrabet K. and Maingot S.]. Elle permet d'obtenir un problème direct et simplifié où l'effet de la couche mince se retrouve complètement décrit par l'opérateur d'impédance. Les techniques employées sont essentiellement basées sur le calcul fonctionnel de Dunford, la théorie des semi-groupes, l'interpolation et quelques idées des travaux de [R. Labbas, Thèse d'état], [Dore G., Favini A., Labbas R., Lemrabet K. and Maingot S.] et [Favini A., Labbas R., Maingot S., Tanabe H., Yagi A.]. On obtient des résultats nouveaux d'existence, d'unicité et de régularité maximale dans les espaces de Hölder pour fixé et ensuite on étudie le passage à la limite quand δ→0 de (Pδ)δ>0. Ce travail complète ainsi ce qui a été obtenu dans le cadre Lp, voir [Favini A., Labbas R., Lemrabet K. and Maingot S.].</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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