## A Convergent Series Expansion for Hyperbolic Systems of Conservation Laws, Volume 172557National Aeronautics and Space Administration, Langley Research Center, 1985 - Differential equations, Hyperbolic |

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A(uQ analytic function Applying Lemma basis of eigenvectors boundary conditions bounded independent characteristic surfaces components conservation laws contact surfaces CONVERGENT SERIES Corollary denote depending on u_ determine end gaps equation to equation estimate in 4.5 Euler equations Figure follows formal power series formulas gap equations genuinely nonlinear field Hence holds HYPERBOLIC SYSTEMS implies impose continuity inequality initial data initial value problem Jacobian Langley Research Center left and right left-hand side Lenma linearly degenerate fields Main Majorization Lemma multiple eigenvalues NASA obtain order coefficients Proof Rankine-Hugoniot conditions rarefaction and sound rarefaction surface Riemann invariants Riemann problem Riemann solution right-hand side satisfy shock surface Similarly sound surface sound waves summing over q surface coefficients surface we impose SYSTEMS OF CONSERVATION T T K term Theorem total number unknown surfaces vector weaker hypothesis Wlth zero order zR)k