Electron. J. Differential Equations,
Vol. 2016 (2016), No. 325, pp. 118.
Existence of solutions for a scalar conservation law with a flux
of low regularity
Martin Lazar, Darko Mitrovic
Abstract:
We prove existence of solutions to Cauchy problem for scalar conservation
laws with nondegenerate discontinuous flux
where for every
,
the flux
and
,
additionally satisfying
,
for some
and every
,
and, for every
,
where
is the space of Radon measures.
Moreover, the function s is measurable and both f and s satisfy certain
growth rate assumptions with respect to
.
The result is obtained
by means of the Hmeasures.
Submitted May 18, 2016. Published December 22, 2016.
Math Subject Classifications: 35L65.
Key Words: Scalar conservation law; discontinuous coefficient; existence;
velocity averaging; Hmeasure.
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Martin Lazar
University of Dubrovnik, Croatia
email: mlazar@unidu.hr


Darko Mitrović
Faculty of Mathematics
University of Montenegro
Montenegro
email: darkom@ac.me

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