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Front Tracking for Hyperbolic Conservation Laws [Hardcover]

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Item Number 229974  
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Item description for Front Tracking for Hyperbolic Conservation Laws by Helge Holden...

Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations, and in many applications in science and technology. In this book the reader is given a detailed, rigorous, and self-contained presentation of the theory of hyperbolic conservation laws from the basic theory up to the research front. The approach is constructive, and the mathematical approach using front tracking can be applied directly as a numerical method. After a short introduction on the fundamental properties of conservation laws, the theory of scalar conservation laws in one dimension is treated in detail, showing the stability of the Cauchy problem using front tracking. The extension to multidimensional scalar conservation laws is obtained using dimensional splitting. Inhomogeneous equations and equations with diffusive terms are included as well as a discussion of convergence rates. The classical theory of Kruzkov and Kuznetsov is covered. Systems of conservation laws in one dimension are treated in detail, starting with the solution of the Riemann problem. Solutions of the Cauchy problem are proved to exist in a constructive manner using front tracking, amenable to numerical computations. The book includes a detailed discussion of the very recent proof of wellposedness of the Cauchy problem for one-dimensional hyperbolic conservation laws. The book includes a chapter on traditional finite difference methods for hyperbolic conservation laws with error estimates and a section on measure valued solutions. Extensive examples are given, and many exercises are included with hints and answers. Additional background material not easily available elsewhere is given in appendices.

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Item Specifications...

Pages   376
Est. Packaging Dimensions:   Length: 8.9" Width: 6.3" Height: 1"
Weight:   1.45 lbs.
Binding  Hardcover
Publisher   Springer
ISBN  3540432892  
ISBN13  9783540432890  

Availability  0 units.

More About Helge Holden

Register your artisan biography and upload your photo! Helge Holden is Professor of Mathematics at the Norwegian University of Science and Technology.

Helge Holden has an academic affiliation as follows - Norwegian Institute of Technology, Trondheim Norwegian University of S.

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Product Categories

1Books > Special Features > New & Used Textbooks > Sciences > Mathematics
2Books > Special Features > New & Used Textbooks > Sciences > Physics
3Books > Subjects > Professional & Technical > Professional Science > Mathematics > Applied > Differential Equations
4Books > Subjects > Professional & Technical > Professional Science > Mathematics > Applied > General
5Books > Subjects > Professional & Technical > Professional Science > Mathematics > Applied > Statistics
6Books > Subjects > Professional & Technical > Professional Science > Physics > Mathematical Physics
7Books > Subjects > Science > General
8Books > Subjects > Science > Mathematics > Applied > Differential Equations
9Books > Subjects > Science > Mathematics > Applied > General
10Books > Subjects > Science > Mathematics > Applied > Probability & Statistics
11Books > Subjects > Science > Mathematics > General
12Books > Subjects > Science > Physics > Mathematical Physics

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