Front Tracking for Hyperbolic Conservation Laws

Etukansi
Springer Science & Business Media, 8.10.2011 - 361 sivua

Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included.

From the reviews:

"It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet

"I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course." S. Noelle, Book review, German Math. Soc.

"Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm.

 

Esimerkkisivuja

Sisältö

1 Introduction
1
2 Scalar Conservation Laws
23
3 A Short Course in Difference Methods
63
4 Multidimensional Scalar Conservation Laws
117
5 The Riemann Problem for Systems
163
6 Existence of Solutions of the Cauchy Problem for Systems
205
7 WellPosedness of the Cauchy Problem for Systems
232
Appendix A Total Variation Compactness etc
287
Appendix B The Method of Vanishing Viscosity
299
Appendix C Answers and Hints
315
References
349
Index
359
Tekijänoikeudet

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Yleiset termit ja lausekkeet

apply approximation argument Assume bounded called Chapter characteristics choose collision compact compute conclude conservation laws consider consists constant construction converges convex curves define denote derivative difference differentiable discontinuity distribution eigenvalues entropy condition entropy solution equal equation estimate Example exists Figure flux function front tracking Furthermore given gives Hence holds hyperbolic implies inequality initial data initial value problem integral interaction interval introduce Lemma limit Lipschitz continuous measure method monotone notation Note Observe obtain piecewise linear positive proof properties prove Rankine–Hugoniot rarefaction wave reads remains respectively result Riemann problem satisfies scalar scheme sequence shock side Similarly smooth solve space speed splitting term test function Theorem total variation unique weak solution write zero

Kirjaluettelon tiedot

OtsikkoFront Tracking for Hyperbolic Conservation Laws
Nide 152 / Applied Mathematical Sciences
KirjailijatHelge Holden, Nils Henrik Risebro
Painoskuvitettu
KustantajaSpringer Science & Business Media, 2011
ISBN3642239110, 9783642239113
Pituus361 sivua
  
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