Cantitate/Preț
Produs

An Introduction to Fronts in Random Media: Surveys and Tutorials in the Applied Mathematical Sciences, cartea 5

Autor Jack Xin
en Limba Engleză Paperback – 13 iul 2009
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.
Citește tot Restrânge

Din seria Surveys and Tutorials in the Applied Mathematical Sciences

Preț: 34082 lei

Nou

Puncte Express: 511

Preț estimativ în valută:
6523 6781$ 5404£

Carte tipărită la comandă

Livrare economică 04-18 februarie 25

Preluare comenzi: 021 569.72.76

Specificații

ISBN-13: 9780387876825
ISBN-10: 0387876820
Pagini: 159
Ilustrații: X, 162 p.
Dimensiuni: 155 x 235 x 8 mm
Greutate: 0.25 kg
Ediția:2009
Editura: Springer
Colecția Springer
Seria Surveys and Tutorials in the Applied Mathematical Sciences

Locul publicării:New York, NY, United States

Public țintă

Research

Cuprins

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.

Textul de pe ultima copertă

This book gives a user friendly tutorial to Fronts in Random Media, an interdisciplinary research topic, to senior undergraduates and graduate students in the mathematical sciences, physical sciences and engineering.
Fronts or interface motion occur in a wide range of scientific areas where the physical and chemical laws are expressed in terms of differential equations. Heterogeneities are always present in natural environments: fluid convection in combustion, porous structures, noise effects in material manufacturing to name a few.
Stochastic models hence become natural due to the often lack of complete data in applications.
The transition from seeking deterministic solutions to stochastic solutions is both a conceptual change of thinking and a technical change of tools. The book explains ideas and results systematically in a motivating manner. It covers multi-scale and random fronts in three fundamental equations (Burgers, Hamilton-Jacobi, and reaction-diffusion-advection equations) and explores their connections and mechanical analogies. It discusses representation formulas, Laplace methods, homogenization, ergodic theory, central limit theorems, large-deviation principles, variational and maximum principles.
It shows how to combine these tools to solve concrete problems.
Students and researchers will find the step by step approach  and the open problems in the book particularly useful.
 

Caracteristici

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