Holdings: Singularly perturbed problems in case of exchange of stabilities

Singularly perturbed problems in case of exchange of stabilities:

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Main Authors:	Butuzov, Valentin F. (Author), Nefedov, Nikolaj N. (Author), Schneider, Klaus R. (Author)
Format:	Book
Language:	English
Published:	Berlin WIAS 2002
Series:	Report / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. 21
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. 144 - 150
Physical Description:	150 S. graph. Darst.

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adam_text	WEIERSTRAFI-INSTITUT FUR ANGEWANDTE ANALYSIS UND STOCHASTIK IM FORSCHUNGSVERBUND BERLIN E.V. SINGULARLY PERTURBED PROBLEMS IN CASE OF EXCHANGE OF STABILITIES VALENTIN F. BUTUZOV 1 , NIKOLAI N. NEFEDOV 1 , KLAUS R. SCHNEIDER 2 SUBMITTED: 24TH APRIL 2002 1 MOSCOW STATE UNIVERSITY 2 WEIERSTRAFIINSTITUT DEPARTMENT OF PHYSICS FUR ANGEWANDTE ANALYSIS VOROB OVI GORI UND STOCHASTIK 119992 MOSCOW MOHRENSTRAFIE 39 RUSSIA 10117 BERLIN E-MAIL: BUTUZOV@PHYS.MSU.SU GERMANY E-MAIL: NEFEDOV@PHYS.MSU.SU E-MAIL: SCHNEIDE@WIAS-BERLIN.DE REPORT NO. 21 BERLIN 2002 2000 MATHEMATICS SUBJECT CLASSIFICATION. 34-0 2, 35-02, 34E15, 34E05, 34A12, 34B15, 35B25, 35J25, 35K57. KEY WORDS AND PHRASES. SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS, ASYMPTOTIC EXPANSIONS, EX- CHANGE OF STABILITIES, DELAYED EXCHANGE OF STABILITIES, INITIAL VALUE PROBLEMS, BOUNDARY VALUE PROB- LEMS, INITIAL-BOUNDARY VALUE PROBLEMS. THIS WORK HAS BEEN SUPPORTED BY RFFI-DFG GRANTS AND BY WIAS. CONTENTS 0 INTRODUCTION 5 0.1 ON THE DEVELOPMENT OF THE THEORY OF SINGULAR PERTURBATIONS 5 0.2 TIKHONOV S FUNDAMENTAL THEOREM ON SINGULARLY PERTURBED SYSTEMS . . 6 0.3 UNIFORM ASYMPTOTICS 8 0.4 EXCHANGE OF STABILITIES IN SINGULARLY PERTURBED PROBLEMS 10 0.5 PROBLEMS OF REACTION KINETICS LEADING TO SINGULARLY PERTURBED DIFFER- ENTIAL EQUATIONS IN CASE OF EXCHANGE OF STABILITIES 13 0.6 THE PHENOMENON OF DELAYED EXCHANGE OF STABILITIES 15 0.7 CONTENT OF THE SURVEY ARTICLE 16 1 INITIAL VALUE PROBLEM FOR SYSTEMS OF TIKHONOV S TYPE 21 1.1 FORMULATION OF THE PROBLEM. ASSUMPTIONS 21 1.2 COMPOSED STABLE SOLUTION OF THE DEGENERATE PROBLEM 23 1.3 ASYMPTOTIC BEHAVIOR OF THE SOLUTION 25 1.4 EXAMPLE: FAST BIMOLECULAR REACTION WITH MONOMOLECULAR SLOW REACTION 30 2 DELAYED EXCHANGE OF STABILITIES FOR ODES 33 2.1 FORMULATION OF THE PROBLEM 33 2.2 ASSUMPTIONS 34 2.3 MAIN RESULTS 37 2.4 EXAMPLES 42 3 BOUNDARY VALUE PROBLEMS FOR SECOND ORDER EQUATIONS 45 3.1 INTRODUCTION 45 3.2 STATEMENT OF THE PROBLEM 48 3.3 CONSTRUCTION OF AN UPPER SOLUTION 49 3.4 CONSTRUCTION OF A LOWER SOLUTION 51 3.5 THE MAIN RESULT 53 3.6 THE CASE WHEN / DEPENDS ON E 54 4 BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF TICHONOV S TYPE 57 4.1 FORMULATION OF THE PROBLEMS 57 4.2 THE COMPOSED STABLE SOLUTION OF THE DEGENERATE PROBLEM FOR (BIVP) . 59 4.3 THE ASYMPTOTIC BEHAVIOR OF THE SOLUTION OF (BIVP) IN CASE WHEN G DEPENDS ONE 61 4.4 (BIVP) IN THE CASE WHEN G DOES NOT DEPEND ONE 65 4.5 THE COMPOSED STABLE SOLUTION OF THE DEGENERATE PROBLEM FOR (BVP) . 77 4.6 THE ASYMPTOTIC BEHAVIOR OF THE SOLUTION OF (BVP) IN THE CASE WHEN G DEPENDS ONE *. 78 4.7 PROBLEM (BVP) IN THE CASE WHEN G DOES NOT DEPEND ONE 84 5 INITIAL BOUNDARY VALUE PROBLEM FOR A PARABOLIC EQUATION 85 5.1 FORMULATION OF THE PROBLEM 85 5.2 ASSUMPTIONS 86 5.3 EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE SOLUTION 88 5.4 EXAMPLE 94 6 DELAYED EXCHANGE OF STABILITIES IN PARABOLIC PROBLEMS 96 6.1 FORMULATION OF THE PROBLEM 96 6.2 ASSUMPTIONS 97 6.3 MAIN RESULTS .100 7 PARTLY DISSIPATIVE REACTION-DIFFUSION SYSTEMS 106 7.1 FORMULATION OF THE PROBLEM 106 7.2 COMPOSED STABLE SOLUTION OF THE DEGENERATE PROBLEM 108 7.3 ASYMPTOTIC BEHAVIOR OF THE SOLUTION ILL 7.4 EXAMPLE 119 7.5 REACTION-DIFFUSION SYSTEM OF TWO PARABOLIC EQUATIONS 121 8 BOUNDARY VALUE PROBLEMS FOR ELLIPTIC EQUATIONS 123 8.1 FORMULATION OF THE PROBLEM. ASSUMPTIONS 123
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author	Butuzov, Valentin F. Nefedov, Nikolaj N. Schneider, Klaus R.
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spelling	Butuzov, Valentin F. Verfasser aut Singularly perturbed problems in case of exchange of stabilities Valentin F. Butuzov ; Nikolai N. Nefedov ; Klaus R. Schneider. Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. Berlin WIAS 2002 150 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Report / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. 21 Literaturverz. S. 144 - 150 Nefedov, Nikolaj N. Verfasser aut Schneider, Klaus R. Verfasser aut Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. Report 21 (DE-604)BV009889758 21 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010178558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Butuzov, Valentin F. Nefedov, Nikolaj N. Schneider, Klaus R. Singularly perturbed problems in case of exchange of stabilities
title	Singularly perturbed problems in case of exchange of stabilities
title_auth	Singularly perturbed problems in case of exchange of stabilities
title_exact_search	Singularly perturbed problems in case of exchange of stabilities
title_full	Singularly perturbed problems in case of exchange of stabilities Valentin F. Butuzov ; Nikolai N. Nefedov ; Klaus R. Schneider. Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V.
title_fullStr	Singularly perturbed problems in case of exchange of stabilities Valentin F. Butuzov ; Nikolai N. Nefedov ; Klaus R. Schneider. Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V.
title_full_unstemmed	Singularly perturbed problems in case of exchange of stabilities Valentin F. Butuzov ; Nikolai N. Nefedov ; Klaus R. Schneider. Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V.
title_short	Singularly perturbed problems in case of exchange of stabilities
title_sort	singularly perturbed problems in case of exchange of stabilities
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010178558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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