FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 5, PAGES 175-188

**On well-posedness classes of locally bounded generalized entropy
solutions of the Cauchy problem for quasilinear first-order equations**

E. Yu. Panov

Abstract

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We study scalar conservation laws with power 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.
We give examples showing that enlargement of the growth exponent leads
to failure of the correctness.

Location: http://mech.math.msu.su/~fpm/eng/k06/k065/k06514h.htm

Last modified: February 21, 2007