| Abstract: | This paper studies isentropic solutions of quasilinear first-order equations with two independent variables and a flux function
that is only continuous. The isentropic solutions are characterized by the requirement that the S. N. Kruzhkov entropy conditions
hold for these solution with the equality sign. It turns out that the existence of a nonconstant isentropic solution imposes
rather strong restrictions on the nonlinearity. In particular, it is shown that on the minimal interval containing the essential
image of the isentropic solution, the flux function satisfies the local Lipschitz condition, and its generalized derivative
is a function of locally bounded variation. Also, it is proved that when the flux function is nonlinear, any isentropic solution
is continuous on nondegenerate intervals.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal
Conference-2004, Part 1, 2005. |
