Partial Differential Equations with Random Initial Data
Gi-Ren Liu
ISBN 10: 3639704762 ISBN 13: 9783639704761
Published by Scholars' Press, 2014
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Partial Differential Equations with Random Initial Data | Gi-Ren Liu | Taschenbuch | 148 S. | Englisch | 2014 | Scholars' Press | EAN 9783639704761 | Verantwortliche Person für die EU: BoD - Books on Demand, In de Tarpen 42, 22848 Norderstedt, info[at]bod[dot]de | Anbieter: preigu. Seller Inventory # 105427323
Synopsis:
We study the limiting distributions of the solution of fractional diffusion-wave systems with subordinated Gaussian random initial data. In our work, we use homogeneous random field to model the initial data and apply the spectral representation method and multiple Wiener integrals to studying the covariance matrix functions of the random solution. The limiting distributions of the solution are obtained from different viewpoints including macroscopic scales and microscopic scales. When the initial data is weakly dependent, our results can be thought of as a generalized central limit theorem. There are two key points for this new result. The first one is that the initial data is modeled by two cross-correlated random fields, which is analyzed by the method of Feynman diagrams. Second, the limit of the solution under the macroscopic/microscopic coordinate systems is represented by a series of mutually independent Gaussian random fields. When the initial data is long-range dependent. We found a competition relationship between the effects coming from the components of the random initial data, i.e., the limiting distribution of the solution is determined by one of the components.
About the Author: Gi-Ren Liu received his Ph.D. degree from National Taiwan University in 2013. Currently, he served as a post-doctoral fellow in Department of Computer Science, National Chiao Tung University. His current research interests include queuing theory, Markov decision processes and their applications on personal communications services.
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Bibliographic Details
Title: Partial Differential Equations with Random ...
Publisher: Scholars' Press
Publication Date: 2014
Binding: Taschenbuch
Condition: Neu