Nonlinear Diffusive Waves

P. L. Sachdev

doi:10.1017/CBO9780511569449

This monograph deals with Burgers' equation and its generalisations. Such equations describe a wide variety of nonlinear diffusive phenomena, for instance, in nonlinear acoustics, laser physics, plasmas and atmospheric physics. The Burgers equation also has mathematical interest as a canonical nonlinear parabolic differential equation that can be exactly linearised. It is closely related to equations that display soliton behaviour and its study has helped elucidate other such nonlinear behaviour. The approach adopted here is applied mathematical. The author discusses fully the mathematical properties of standard nonlinear diffusion equations, and contrasts them with those of Burgers' equation. Of particular mathematical interest is the treatment of self-similar solutions as intermediate asymptotics for a large class of initial value problems whose solutions evolve into self-similar forms. This is achieved both analytically and numerically.

- Aa Reduce text
- Aa Enlarge text

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to .

To save content items to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services

Metrics

Total number of HTML views: 0

Total number of PDF views: 0 *

Loading metrics...

Total views: 0 *

Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Why this information is here

This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

Accessibility Information

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.

Nonlinear Diffusive Waves

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Book description

Refine List

Actions for selected content:

Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

1 - Introduction and overview
pp 1-5

2 - The Burgers equation
pp 6-39

3 - Generalised Burgers equations
pp 40-97

4 - Self-similar solutions as intermediate asymptotics for nonlinear diffusion equations
pp 98-152

5 - Numerical solution of nonlinear diffusion equations
pp 153-230

References
pp 231-240

Author index
pp 241-243

Subject index
pp 244-246

Metrics

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information

Nonlinear Diffusive Waves

Book description

Refine List

Actions for selected content:

Save Search

Contents

Metrics

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information