Skip to main content
SpringerLink
Log in
Book cover

An Introduction to Fronts in Random Media

  • Textbook
  • © 2009

Overview

Authors:
  1. Jack Xin
    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Many exercises and examples
  • Expository style of writing
  • Includes supplementary material: sn.pub/extras

Part of the book series: Surveys and Tutorials in the Applied Mathematical Sciences (STAMS, volume 5)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (5 chapters)

  1. Front Matter

    Pages 1-9
    Download chapter PDF

  2. Fronts in Homogeneous Media

    • Jack Xin
    Pages 1-21

  3. Fronts in Periodic Media

    • Jack Xin
    Pages 23-51

  4. Fronts in Random Burgers Equations

    • Jack Xin
    Pages 53-67

  5. Fronts and Stochastic Homogenization of Hamilton–Jacobi Equations

    • Jack Xin
    Pages 69-92

  6. KPP Fronts in Random Media

    • Jack Xin
    Pages 93-144

  7. Back Matter

    Pages 1-14
    Download chapter PDF
Back to top

Keywords

About this book

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.

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation