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On well-posedness classes of locally bounded generalized entropy solutions of the Cauchy problem for quasilinear first-order equations. (English) Zbl 1151.35399

J. Math. Sci., New York 150, No. 6, 2578-2587 (2008); translation from Fundam. Prikl. Mat. 12, No. 5, 175-188 (2006).
Summary: We study scalar conservation laws with power-growth restriction on the flux vector. For such equations, we find correctness classes for the Cauchy problem among locally bounded generalized entropy solutions. These classes are determined by some exponents of admissible growth with respect to space variables. We give examples showing that increasing the growth exponent leads to failure of the well-posedness.

MSC:

35L65 Hyperbolic conservation laws
35L45 Initial value problems for first-order hyperbolic systems
35B25 Singular perturbations in context of PDEs
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