The Cauchy Problem in Kinetic Theory

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $74.34
Usually ships in 1-2 business days
Other sellers (Paperback)
  • All (4) from $74.34   
  • New (3) from $74.34   
  • Used (1) from $74.86   
Sort by
Page 1 of 1
Showing All
Note: Marketplace items are not eligible for any coupons and promotions
Seller since 2008

Feedback rating:



New — never opened or used in original packaging.

Like New — packaging may have been opened. A "Like New" item is suitable to give as a gift.

Very Good — may have minor signs of wear on packaging but item works perfectly and has no damage.

Good — item is in good condition but packaging may have signs of shelf wear/aging or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Acceptable — item is in working order but may show signs of wear such as scratches or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Used — An item that has been opened and may show signs of wear. All specific defects should be noted in the Comments section associated with each item.

Refurbished — A used item that has been renewed or updated and verified to be in proper working condition. Not necessarily completed by the original manufacturer.

New Book. Shipped from UK within 10 to 14 business days. Established seller since 2000.

Ships from: Horcott Rd, Fairford, United Kingdom

Usually ships in 1-2 business days

  • Standard, 48 States
  • Standard (AK, HI)
Seller since 2008

Feedback rating:


Condition: New
Brand New, Perfect Condition, Please allow 4-14 business days for delivery. 100% Money Back Guarantee, Over 1,000,000 customers served.

Ships from: Westminster, MD

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
Seller since 2015

Feedback rating:


Condition: New
Brand New Item.

Ships from: Chatham, NJ

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
  • Express, 48 States
  • Express (AK, HI)
Page 1 of 1
Showing All
Sort by


This clearly written, self-contained volume studies the basic equations of kinetic theory in all of space. It contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations, including the Boltzmann equation (from rarefied gas dynamics) and the Vlasov-Poisson/Vlasov-Maxwell systems (from plasma physics). This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although these equations describe very different phenomena, they share the same streaming term. The author proves that solutions starting from a given configuration at an initial time exist for all future times by imposing appropriate hypotheses on the initial values in several important cases. He emphasizes those questions that a mathematician would ask first: Is there a solution to this problem? Is it unique? Can it be numerically approximated?
Read More Show Less

Editorial Reviews

From the Publisher
'The book will make a very valuable addition to the bookshelf of every researcher in mathematical kinetic theory.' Reinhard Ilner, SIAM Review
Developed from lecture notes for a course in kinetic theory introducing mathematics faculty and advanced graduate students to the study of the Cauchy problem for the Boltzmann and Vlasov equations. Gathers the desired results on both equations from the scattered literature. Assumes less background and attempts less generality than other treatments. Annotation c. Book News, Inc., Portland, OR (
Andrzej Palczewski
An unquestionable virtue of the book is its part devoted to the Vlasov equation. Such a complete mathematical theory of different kinetic models for charged particles I have not seen before.
Mathematical Reviews
Reinhard Ilner
"The book will make a very valuable addition to the bookshelf of every researcher in mathematical kinetic theory."
SIAM Review
Read More Show Less

Product Details

  • ISBN-13: 9780898713671
  • Publisher: SIAM
  • Publication date: 1/28/1996
  • Series: Miscellaneous Titles Series
  • Pages: 241
  • Product dimensions: 5.98 (w) x 8.98 (h) x 0.67 (d)

Table of Contents

Preface; 1. Properties of the Collision Operator. Kinetic Theory, Derivation of the Equations, The Form of the Collision Operator, The Hard Sphere Case, Conservation Laws and the Entropy, Relevance of the Maxwellian, The Jacobian Determinant, The Structure of Collision Invariants, Relationship of the Boltzmann Equation to the Equations of Fluids, References; 2. The Boltzmann Equation Near the Vacuum. Invariance of $|x-tv|^2+|x-tu|^2$, Sequences of Approximate Solutions, Satisfaction of the Beginning Condition, Proof that $u=\ell$, Remarks and Related Questions, References; 3. The Boltzmann Equation Near the Equilibrium. The Perturbation from Equilibrium, Computation of the Integral Operator, Estimates on the Integral Operator, Properties of $L$, Compactness of $K$, Solution Spaces, An Orthonormal Basis for $N(L)$, Estimates on the Nonlinear Term, Equations for 13 Moments, Computation of the Coefficient Matrices, Compensating Functions, Time Decay Estimates, Time Decay in Other Norms, The Major Theorem, The Relativistic Boltzmann Equation, References; 4. The Vlasov--Poisson System. Introduction, Preliminaries and A Priori Estimates, Sketch of the Existence Proof, The Good, the Bad and the Ugly, The Bound on the Velocity Support, Blow-up in the Gravitational Case, References; 5. The Vlasov--Maxwell System. Collisionless Plasmas, Control of Large Velocities, Representation of the Fields, Representation of the Derivatives of the Fields, Estimates on the Particle Density, Bounds on the Field, Bounds on the Gradient of the Field, Proof of Existence, References; 6. Dilute Collisionless Plasmas. The Small--data Theorem, Outline of the Proof, Characteristics, The Particle Densities, Estimates on the Fields, Estimates on Derivatives of the Fields, References; 7. Velocity Averages: Weak Solutions to the Vlasov--Maxwell System. Sketch of the Problem, The Velocity Averaging Smoothing Effect, Convergence of the Current Density, Completion of the Proof, References; 8. Convergence of a Particle Method for the Vlasov--Maxwell System. Introduction, The Particle Simulation, The Field Errors, The Particle Errors, Summing the Errors, References; Index.
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)