Hyperbolic Systems of Conservation Laws in Several Space Variables

Cover Hyperbolic Systems of Conservation Laws in Several Space Variables
Hyperbolic Systems of Conservation Laws in Several Space Variables
Peter D Lax
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4) genuinely nonlinear if the equations (2. 6) for unidirectional waves are genuinely nonlinear for every choice of the direction.
Take a scalar equation ^t * ^"X + t)Uy =, a, b functions of u; equation (2. 6) is W^_ + C Wg =, c = Ca + nb . Condition (2. 3)' becomes Ca^ + nb^ ?t, clearly violated by suitable choice of (C, '^). Thus a scalar quasilinear equation in two space variables is never genuinely nonlinear in all directions.
We turn now to the 2x2 system (1. 4)'. We write i. E.
-10- a + i
...b = qe^'t' a = q cos , b = q sin

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