Philippe G. Lefloch

Hyperbolic Systems of Conservation Laws (eBook, PDF)

The Theory of Classical and Nonclassical Shock Waves

• Format: PDF

Produktbeschreibung

This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions. It also introduces the reader to the developing theory of nonclassical (undercompressive) entropy solutions. The systems of partial differential equations under consideration arise in many areas of continuum physics.

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Produktdetails

• Verlag: Birkhäuser Basel
• Seitenzahl: 294
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783034881500
• Artikelnr.: 53107680

Autorenporträt

LeFloch, P.G., Ecole Polytechnique, Palaiseau, France

Inhaltsangabe

I. Fundamental concepts and examples.- 1. Hyperbolicity, genuine nonlinearity, and entropies.- 2. Shock formation and weak solutions.- 3. Singular limits and the entropy inequality.- 4. Examples of diffusive-dispersive models.- 5. Kinetic relations and traveling waves.- 1. Scalar Conservation Laws.- II. The Riemann problem.- III. Diffusive-dispersive traveling waves.- IV. Existence theory for the Cauchy problem.- V. Continuous dependence of solutions.- 2. Systems of Conservation Laws.- VI. The Riemann problem.- VII. Classical entropy solutions of the Cauchy problem.- VIII. Nonclassical entropy solutions of the Cauchy problem.- IX. Continuous dependence of solutions.- X. Uniqueness of entropy solutions.