Electron. J. Diff. Eqns., Vol. 2007(2007), No. 114, pp. 1-22.

Global solution to a Hopf equation and its application to non-strictly hyperbolic systems of conservation laws

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
email: mitrovic@math.ntnu.no
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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