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2016 | OriginalPaper | Buchkapitel

Evolution Solutions of Equilibrium Problems: A Computational Approach

verfasst von : Monica-Gabriela Cojocaru, Scott Greenhalgh

Erschienen in: Mathematical Analysis, Approximation Theory and Their Applications

Verlag: Springer International Publishing

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Abstract

This paper proposes a computational method to describe evolution solutions of known classes of time-dependent equilibrium problems (such as time-dependent traffic network, market equilibrium or oligopoly problems, and dynamic noncooperative games). Equilibrium solutions for these classes have been studied extensively from both a theoretical (regularity, stability behaviour) and a computational point of view. In this paper we highlight a method to further study the solution set of such problems from a dynamical systems perspective, namely we study their behaviour when they are not in an (market, traffic, financial, etc.) equilibrium state. To this end, we define what is meant by an evolution solution for a time-dependent equilibrium problem and we introduce a computational method for tracking and visualizing evolution solutions using a projected dynamical system defined on a carefully chosen L ²-space. We strengthen our results with various examples.

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Vorheriges Kapitel An Adaptive Finite Element Method for Solving a Free Boundary Problem with Periodic Boundary Conditions in Lubrication Theory

Nächstes Kapitel Cantor, Banach and Baire Theorems in Generalized Metric Spaces

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Titel: Evolution Solutions of Equilibrium Problems: A Computational Approach
verfasst von: Monica-Gabriela Cojocaru
Scott Greenhalgh
Verlag: Springer International Publishing
Buch: Mathematical Analysis, Approximation Theory and Their Applications
Print ISBN: 978-3-319-31279-8

Electronic ISBN: 978-3-319-31281-1

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-3-319-31281-1_6

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