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Scalar conservation laws in several spa- sults find their natural place in a clear broad context so tial dimensions are treated in Chapter 6. To focus the that their comprehension is enforced. Along this gen- attention on the essential properties, the homogeneous eral guideline, the book opens Chapter 1 with the case is treated explicitly: the inhomogeneous one can be tackled along the same guidelines at the expense P.

Systems of one-dimensional conservation shocks. Such a method is called the front tracking simple waves; genuine nonlinearity and its role in the method. Details analyses of in Chapter 14 for scalar balance laws and their gen- admissible shocks for systems of one-dimensional bal- uinely nonlinear strictly hyperbolic systems.

Essential ance laws are matter of Chapter 8. Chapter 9 opens issues of the vanishing viscosity method are presented with the introduction of the concept of self-similar so- in Chapter The effects of the presence of small lutions to systems of conservation laws: they are in- diffusion are investigated as the diffusion itself van- variant under uniform deformation of the space-time ishes. Solutions can be interpreted as trajectories of tube.

Such solutions can be depicted, in general, as an L1 -Lipshitz semigroup.

### Recensie(s)

The method works in gen- waves converging to a focus and interacting there. For large initial data even weak solutions to the Riemannian problem is treated via wave fan curves. Cauchy problem may blow up in finite time. The rea- The chapter includes also essential remarks about gen- son is still unknown.

## Hyperbolic Conservation Laws in Continuum Physics

In a limited class of cases, so- uine nonlinearity, viscosity of wave fans and their in- lutions with large initial data can be constructed by teraction. Measure-valued solutions are involved. Solutions sions.

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The notion of characteristic is extended to the are constructed as limits of approximate solutions for framework of BV solutions in Chapter These gen- which only boundedness in some Lp space is required. Genuine nonlinear scalar oscillations by means of entropy inequalities. Previ- conservation laws are treated in Chapter 11 the title ously unpublished results of the author enrich the trea- of the chapter is completely self-explanatory.

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Learn how we and our ad partner Google, collect and use data. His masterly written book is, surely, the most complete exposition in the subject of conservations laws. The statements of theorems are carefully and precisely written. The proofs are canonical and illuminating ….

This book is sure to convince every reader that working in this area is challenging, enlightening, and joyful. I heartily recommend this book to anyone who wants to learn about the foundations of the theory of balance and conservation laws and their generic relations to continuum physics …. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Grundlehren der mathematischen Wissenschaften Free Preview. Show next edition.

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Buy eBook. FAQ Policy. About this book This masterly exposition of the mathematical theory of hyperbolic system for conservation laws brings out the intimate connection with continuum thermodynamics, by emphasising issues in which the analysis may reveal something about the physics and, in return, the underlying physical structure may direct and drive the analysis.

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