Smooth Solutions Of Partially Aligned Systems Of Conservation Laws

We discuss smooth solutions for a class of quasilinear non-strictly hyperbolic 2 x 2 systems in two space dimensions that have a distinct characteristic structure consisting of pairs of curves through each point in physical space. We survey the elementary properties of these systems, present an example of interest for certain applications and describe new results about propagation of support, singularity formation and outline a description of the causality structure as an application of control theory techniques.76SUPPL. 2141144Dafermos, C., (1993) Entropy for Hyperbolic Systems of Conservation Laws in Several Space Dimensions, , Brown U. preprint LCDS #93-15Daripa, P., Polymer floods: A case study of nonlinear wave analysis and of instability control in tertiary oil recovery. Research and Development report (1986) OER-Applied Math.Sci., , subprogramKeyfitz, B.L., A survey of nonstrictly hyperbolic conservation laws (1987) Lecture Notes in Mathematics, 1270, pp. 152-162. , Springer VerlagKrener, A., Schättler, H., The structure of small-time reachable sets in low dimensions (1989) SIAM J. Control Opt., 27 (1), pp. 120-147Lobry, Controlabilite des sistemes non lineares (1970) SIAM J. Control, 8 (4), pp. 573-605Lopes Filho, M.C., Nussenzveig Lopes, H.J., Multidimensional hyperbolic systems with degenerate characteristic structure (1995) Matematica Contemporanea, 8, pp. 225-238Lopes Filho, M.C., Nussenzveig Lopes, H.J., Singularity formation for a system of conservation laws in two space dimensions (1995) J. Math. Anal. Apl., , to appearRauch, J., BV estimates fail for most quasilinear systems in dimension greater than one (1986) Comm. Math. Phys., 106, pp. 481-484Sideris, T., Formation of singularities in solutions to nonlinear hyperbolic equations (1984) Arch. Rat. Mech. and Anal., 86 (4), pp. 369-382Strang, G., On Strong Hyperbolicity (1967) J. Math. Kyoto Univ., 6 (3), pp. 397-417Tan, D., Zhang, T., Two-dimensional Riemann problem for a hyperbolic system of conservation laws (1991) Acta Math. Sci. (English Ed.), 11 (4), pp. 369-39