Titlebook: Hyperbolic Systems of Conservation Laws; The Theory of Classi Philippe G. LeFloch Book 2002 Springer Basel AG 2002 Partial differential equ

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Existence Theory for the Cauchy Problem an existence result for the Cauchy problem when the flux-function is .. We exhibit a solution given by an explicit formula (Theorem 1.1) and prove the uniqueness of this solution (Theorem 1.3). The approach developed in Section 1 is of particular interest as it reveals important features of classic

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Nonclassical Entropy Solutions of the Cauchy Problemharacteristic fields are genuinely nonlinear or concave-convex. (The result can be extended to linearly degenerate and convex-concave fields as well.) The proof is based on a generalization of the algorithm described in Chapter VII. Here, we use the nonclassical Riemann solver based on a given kinet

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Continuous Dependence of Solutionsecewise approximate solutions and we refer to Chapter X for a discussion of the uniqueness of . solutions with bounded variation. In Section 1 we outline a general strategy based on a ... for a class of linear hyperbolic systems with discontinuous coefficients. The main result in Theorem 1.5 shows t

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Uniqueness of Entropy Solutionsed variation, slightly restricted by the so-called . (Definition 1.1). The results of existence and continuous dependence established in previous chapters covered solutions obtained as limits of piecewise constant approximate solutions with uniformly bounded total variation (in Chapters IV and V for

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Existence Theory for the Cauchy Problemlem, respectively; see Theorems 2.1 and 3.2 respectively. Finally in Section 4, we derive . for the total variation of solutions (Theorems 4.1 to 4.3) which represent a preliminary step toward the forthcoming discussion of the Cauchy problem for systems (in Chapters VII and VIII).

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