Titlebook: Hyperbolic Conservation Laws in Continuum Physics; Constantine M. Dafermos Book 20001st edition Springer-Verlag Berlin Heidelberg 2000 Bou

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Generalized Characteristics,., since it is within its confines that one may discern shocks and study their propagation and interactions. The notion of characteristic, introduced in Section 7.2 for classical solutions, will here be extended to the framework of . weak solutions. It will be established that generalized characteri

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Genuinely Nonlinear Scalar Conservation Laws,serves attention, not only for its intrinsic interest, but also because it provides valuable insight in the behavior of systems. The discussion here will employ the theory of generalized characteristics developed in Chapter X. From the standpoint of this approach, the special feature of genuinely no

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Genuinely Nonlinear Systems of Two Conservation Laws,recision comparable to that for genuinely nonlinear scalar conservation laws, expounded in Chapter X1. This will be achieved by exploiting the presence of coordinate systems of Riemann invariants and the induced rich family of entropy-entropy flux pairs. The principal tools in the investigation will

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The Random Choice Method,property, which applies not only to the solutions themselves but even to their approximations by means of vanishing viscosity, layering, relaxation, etc. For systems, however, the situation is different: ..-contraction no longer applies; in its place, ..-Lipschitz continuity will eventually be estab

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The Front Tracking Method and Standard Riemann Semigroups,g 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. The random choice method, expounded in Chapter XIII, side-steps this difficulty by

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Book 20001st edition so-called "extensive quantities", such as mass, momentum and energy, are monitored through the fields of their densities, which are related by balance laws and constitutive equations. A self-contained, though skeletal, introduction to this branch of classical physics is presented in Chapter II. The

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The Front Tracking Method and Standard Riemann Semigroups,any rarefaction wave may be approximated arbitrarily close by fans of (inadmissible) shocks of very small strength. The expectation is that in the limit, as this approximation becomes finer, one recovers admissible solutions.

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Constantine M. Dafermosand mathematical evidence is on the borderline between judgement and belief..However, this is not a unique situation as there are other fields in which the judge has to believe rather than fully understand the expert..The rapid developments in the positive proof of paternity, especially since 1970,