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VDM Verlag Analysis und Numerik von Attraktoren für die Finite-Elemente-Methode: Ein Modellattraktor für eine parabolische Differentialgleichung

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Description

Attraktoren semilinearer parabolischer Differentialgleichungen treten in einer Vielzahl naturwissenschaftlicher und medizinischer Anwendungen auf und lassen sich leider nur selten analytisch berechnen. Daher greift man in der Praxis zu deren Approximation häufig auf numerischen Verfahren zurück. Dieses Werk präsentiert nach einer kurzen Einführung mit Anwendungsgebieten eine umfassende Existenz- und Regularitätstheorie für polynomial beschränkte Nichtlinearitäten. Darauf aufbauend werden Existenz-, Konsitenz-, Stabilitäts- und Konvergenzaussagen für die Finite-Elemente-Methode sowie für das implizite Euler-Verfahren hergeleitet. Für zusätzlich dissipative Nichtlinearitäten wird mittels Lyapunov-Funktionalen und absorbierenden Mengen die Existenz und Oberhalbstetigkeit des globalen Attraktors nachgewiesen. Das letzte Kapitel enthält als Anwendungsbeispiel die Chafee-Infante-Gleichung, deren Bifurkationsanalyse, eine ausführliche Herleitung der Gleichungssysteme sowie zahlreiche mittels GAIO und MATCONT erzielte numerische Resultate. Der umfangreiche Anhang sämtlicher für das Verständnis der Arbeit notwendigen Grundlagen bietet dem Leser alle erforderlichen Hilfsmittel.

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
29 December 2010
Listed Since
30 December 2010

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