Distributions in the physical and engineering sciences. Volume 2: Linear and nonlinear dynamics in continuous media
type: Item
instance of: scholarly article
title: Distributions in the physical and engineering sciences. Volume 2: Linear and nonlinear dynamics in continuous media
zbMATH Open document ID: 1283.46001
author: Alexander I. Saichev
author: Wojbor A. Woyczyński
published in: Applied and Numerical Harmonic Analysis
publication date: 2013-05-10T00:00:00Z
review text: This book follows [Volume 1 (1977; Zbl 0880.46028)] as the second of a series of three volumes. The present volume, ``Linear and nonlinear dynamics in continuous media'', contains Part III, ``Potentials, diffusions, and waves'' and Part IV, ``Nonlinear partial differential equations''. Part III consists of three chapters: Potential theory and fundamental solutions of elliptic equations; Diffusion and parabolic evolution equations; Waves and hyperbolic equations. Part IV is divided into four chapters: First-order nonlinear PDEs and conservation laws; Generalized solutions of first-order nonlinear PDEs; Nonlinear waves and growing interfaces: 1-D Burgers and Kardar-Parisi-Zhang models. Many exercises are proposed at the end of each chapter. The authors point out that many of them are really small research projects. Solutions to all of them are included in Appendix A. The book will be useful to graduate students and researchers who are interested in the applications of distributions and partial differential equations to the applied sciences.
reviewed by: Denise Huet
Mathematics Subject Classification ID: 46-01
Mathematics Subject Classification ID: 35-01
Mathematics Subject Classification ID: 31-02
Mathematics Subject Classification ID: 46F99
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 70-01
Mathematics Subject Classification ID: 76-01
zbMATH DE Number: 6162126
zbMATH Keywords: potential theory
zbMATH Keywords: elliptic equations
zbMATH Keywords: parabolic equations
zbMATH Keywords: hyperbolic equations
zbMATH Keywords: nonlinear partial differential equations
zbMATH Keywords: conservation laws
zbMATH Keywords: flows in porous media
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6162126