Darko Mitrovic, Jela Susic
Abstract:
From a Hopf equation we develop a recently introduced technique, the
weak asymptotic method, for describing the shock wave formation and
the interaction processes. Then, this technique is applied to a
system of conservation laws arising from pressureless gas dynamics.
As an example, we study the shock wave formation process in a
two-dimensional scalar conservation laws arising in oil reservoir
problems.
Submitted December 5, 2006. Published August 22, 2007.
Math Subject Classifications: 35L65.
Key Words: Weak asymptotic method; Hopf equation; shock wave formation;
pressureless gas dynamics; system of conservation laws;
multidimensional shocks.
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Darko Mitrovic Department of Mathematical Sciences Norwegian Institute of Science and Technology Alfred Getz vei 1, NO-7491 Trondheim, Norway email: mitrovic@math.ntnu.no |
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Jela Susic Faculty of Mathematics and Natural Sciences University of Montenegro 81000 Podgorica, Montenegro email: jela@rc.pmf.cg.ac.yu |
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