Abstract: 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.
Conservation Laws Preprint Server <conservation@math.ntnu.no> Last modified: Mon Jan 3 17:41:58 MET 2005