An Introduction to Fronts in Random Media
Series: Surveys and Tutorials in the Applied Mathematical Sciences; 5;
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Product details:
- Edition number 2009
- Publisher Springer New York
- Date of Publication 13 July 2009
- Number of Volumes 1 pieces, Book
- ISBN 9780387876825
- Binding Paperback
- No. of pages162 pages
- Size 235x155 mm
- Weight 550 g
- Language English
- Illustrations X, 162 p. 0
Categories
Long description:
This book aims to give a user friendly tutorial of an interdisciplinary research topic (fronts or interfaces in random media) to senior undergraduates and beginning grad uate students with basic knowledge of partial differential equations (PDE) and prob ability. The approach taken is semiformal, using elementary methods to introduce ideas and motivate results as much as possible, then outlining how to pursue rigor ous theorems, with details to be found in the references section. Since the topic concerns both differential equations and probability, and proba bility is traditionally a quite technical subject with a heavy measure theoretic com ponent, the book strives to develop a simplistic approach so that students can grasp the essentials of fronts and random media and their applications in a self contained tutorial. The book introduces three fundamental PDEs (the Burgers equation, Hamilton– Jacobi equations, and reaction–diffusion equations), analysis of their formulas and front solutions, and related stochastic processes. It builds up tools gradually, so that students are brought to the frontiers of research at a steady pace. A moderate number of exercises are provided to consolidate the concepts and ideas. The main methods are representation formulas of solutions, Laplace meth ods, homogenization, ergodic theory, central limit theorems, large deviation princi ples, variational principles, maximum principles, and Harnack inequalities, among others. These methods are normally covered in separate books on either differential equations or probability. It is my hope that this tutorial will help to illustrate how to combine these tools in solving concrete problems.
MoreTable of Contents:
Fronts in Homogeneous Media.- Fronts in Periodic Media.- Fronts in Random Burgers Equations.- Fronts and Stochastic Homogenization of Hamilton#x2013;Jacobi Equations.- KPP Fronts in Random Media.
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