Darko Mitrovic, Jela Susic
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
| Jela Susic |
Faculty of Mathematics and Natural Sciences
University of Montenegro
81000 Podgorica, Montenegro
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