Titlebook: Hyperbolic Conservation Laws in Continuum Physics; Constantine M. Dafermos Book 2016Latest edition Springer-Verlag Berlin Heidelberg 2016

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The , Theory for Scalar Conservation Laws,ons, the elementary, yet effective, method of characteristics yields a sharper version of Theorem 5.1.1, determining explicitly the life span of solutions with Lipschitz continuous initial data and thereby demonstrating that in general this life span is finite. Thus one must deal with weak solutions

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Hyperbolic Systems of Balance Laws in One-Space Dimension,cessity: At the present time the theory of multidimensional systems is terra incognita, replete with fascinating problems. In any event, the reader should bear in mind that certain multidimensional phenomena, with special symmetry, such as wave focussing, may be studied in the context of the one-spa

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Genuinely Nonlinear Systems of Two Conservation Laws,recision comparable to that for genuinely nonlinear scalar conservation laws, expounded in Chapter XI. This will be achieved by exploiting the presence of coordinate systems of Riemann invariants and the induced rich family of entropy-entropy flux pairs.

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The Front Tracking Method and Standard Riemann Semigroups,the waves and monitoring their interactions as they collide. Interactions between shocks are easily resolved by solving Riemann problems; this is not the case, however, with interactions involving rarefaction waves.

Chronological

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, Solutions for Systems of Balance Laws,systems of balance laws. Thus, this chapter may be viewed as the counterpart of Sect. 5.5, where the same issues are addressed in the context of classical solutions. For the reasons presented in the preceding chapters, the investigation shall be confined to systems in a single spatial dimension and

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