On Correctness Classes of Locally Bounded Generalized Entropy Solutions to
Cauchy Problem for First Order Quasilinear Equations
E. Yu. Panov
We study scalar conservation laws with power-like growth restriction on the
flux vector. For such equations we found 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. Example are given, which show that enlargement of the growth
exponent leads to failure of the correctness, neither uniqueness nor existence
of a solution remains valid.
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- E. Yu. Panov,
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January 1 2005.
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