Documents disponibles écrits par cet auteur

Differential equations with operator coefficients / Vladimir Kozlov

Public ISBD Titre : Differential equations with operator coefficients : with applications to boundary value problems for partial differential equations Type de document : texte imprimé Auteurs : Vladimir Kozlov, Auteur ; Vladimir Maz'ya, Auteur Editeur : Berlin Heidelberg : Springer-Verlag Année de publication : 1999 Collection : Springer Monographs in Mathematics Importance : 440 p. Présentation : couv. ill. en coul. Format : 24 cm. ISBN/ISSN/EAN : 978-3-540-65119-2 Langues : Anglais (eng) Catégories : MATHEMATIQUES Mots-clés : Banach Space, Boundary value problem ,Differential operator, Eigenvalue, Ordinary differential equations with operator coefficients, asymptotics of solutions, differential equation ,ordinary differential equation,partial di, partial differential equation,ordinary differential equations Index. décimale : 04-08 Mathématiques appliquées Résumé : This book is the first systematic and self-contained presentation of a theory of arbitrary order ordinary differential equations with unbounded operator coefficients in a Hilbert or Banach space, developed over the last 10 years by the authors. It deals with conditions of solvability, classes of uniqueness, estimates for solutions and asymptotic representations of solutions at infinity. The authors show how the classical asymptotic theory of ODEs. with scalar coefficients can be extended to very general equations with unbounded operator coefficients. In contrast to other works the authors' approach enables them to obtain asymptotic formulae for solutions under weak conditions on the coefficients of equations. The abstract results are complemented by many new applications to the theory of partial differntial equations. In appendix a systematic treatment of the theory of holomorphic operator functions is given. Note de contenu : Table of contents Part I Differential Equations with Constant Operator Coefficients 1. Power-Exponential Zeros 2. Differential Operator Equations in Weighted Sobolev Spaces 3. Solutions in a Local Sobolev Space 4. Two-Weight L2-Estimates Part II. Differential Equations with Variable Operator Coefficients 5. Existence, Uniqueness and “Pointwise” Estimates 6. Corollaries of Previous Results Under Special Assumptions on L(t, Dt) 7. Two-Weight L2-Estimates for Equations with Variable Coefficients 8. Connection of Solutions Corresponding to Different Strips 9. Applications to the Case of Perturbations Vanishing at Infinity 10.Variants and Extensions of the Previous Theory Part III Asymptotic Theory of Operator Differential Equations 11.Complete Asymptotic Expansions Under Exponential and Power Perturbations of A(Dt) 12.Reduction to a First Order System 13.General Asymptotic Representation 14.Power-Exponential Asymptotics 15.The Case of One Simple Eigenvalue on the Line 16.Several Simple Eigenvalues on the Line 17.The Case of a Single Multiple Eigenvalue A. Holomorphic Operator Functions References Index of Notation Index Index of Names Differential equations with operator coefficients : with applications to boundary value problems for partial differential equations [texte imprimé] / Vladimir Kozlov, Auteur ; Vladimir Maz'ya, Auteur . - Berlin Heidelberg : Springer-Verlag, 1999 . - 440 p. : couv. ill. en coul. ; 24 cm.. - (Springer Monographs in Mathematics) . ISBN : 978-3-540-65119-2 Langues : Anglais (eng) Catégories : MATHEMATIQUES Mots-clés : Banach Space, Boundary value problem ,Differential operator, Eigenvalue, Ordinary differential equations with operator coefficients, asymptotics of solutions, differential equation ,ordinary differential equation,partial di, partial differential equation,ordinary differential equations Index. décimale : 04-08 Mathématiques appliquées Résumé : This book is the first systematic and self-contained presentation of a theory of arbitrary order ordinary differential equations with unbounded operator coefficients in a Hilbert or Banach space, developed over the last 10 years by the authors. It deals with conditions of solvability, classes of uniqueness, estimates for solutions and asymptotic representations of solutions at infinity. The authors show how the classical asymptotic theory of ODEs. with scalar coefficients can be extended to very general equations with unbounded operator coefficients. In contrast to other works the authors' approach enables them to obtain asymptotic formulae for solutions under weak conditions on the coefficients of equations. The abstract results are complemented by many new applications to the theory of partial differntial equations. In appendix a systematic treatment of the theory of holomorphic operator functions is given. Note de contenu : Table of contents Part I Differential Equations with Constant Operator Coefficients 1. Power-Exponential Zeros 2. Differential Operator Equations in Weighted Sobolev Spaces 3. Solutions in a Local Sobolev Space 4. Two-Weight L2-Estimates Part II. Differential Equations with Variable Operator Coefficients 5. Existence, Uniqueness and “Pointwise” Estimates 6. Corollaries of Previous Results Under Special Assumptions on L(t, Dt) 7. Two-Weight L2-Estimates for Equations with Variable Coefficients 8. Connection of Solutions Corresponding to Different Strips 9. Applications to the Case of Perturbations Vanishing at Infinity 10.Variants and Extensions of the Previous Theory Part III Asymptotic Theory of Operator Differential Equations 11.Complete Asymptotic Expansions Under Exponential and Power Perturbations of A(Dt) 12.Reduction to a First Order System 13.General Asymptotic Representation 14.Power-Exponential Asymptotics 15.The Case of One Simple Eigenvalue on the Line 16.Several Simple Eigenvalues on the Line 17.The Case of a Single Multiple Eigenvalue A. Holomorphic Operator Functions References Index of Notation Index Index of Names

Exemplaires

Code-barres	Cote	Support	Localisation	Section	Disponibilité	N.Inventaire
492	04-08-06	Livre	Bibliothèque de Génie Electrique- USTO	Documentaires	Exclu du prêt	492