Global solution to a Hopf equation and its application to non-strictly hyperbolic systems of conservation laws
Texas State University-San Marcos, Department of Mathematics
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.
Weak asymptotic method, Hopf equation, Shock wave formation, Pressureless gas dynamics, System of conservation laws, Multidimensional shocks
Mitrovic, D., & Susic, J. (2007). Global solution to a Hopf equation and its application to non-strictly hyperbolic systems of conservation laws. <i>Electronic Journal of Differential Equations, 2007</i>(114), pp. 1-22.