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A convergent series expansion for hyperbolic systems of conservation laws. (English) Zbl 0599.35103
We consider the discontinuous piecewise analytic initial value problem for a wide class of conservation laws that includes the full three- dimensional Euler equations. The initial interaction at an arbitrary curved surface is resolved in time by a convergent series. Among other features the solution exhibits shock, contact, and expansion waves as well as sound waves propagating on characteristic surfaces. The expansion waves correspond to the one-dimensional rarefactions but have a more complicated structure. The sound waves are generated in place of zero strength shocks, and they are caused by mismatches in derivatives.

35L65 Hyperbolic conservation laws
35A10 Cauchy-Kovalevskaya theorems
35A20 Analyticity in context of PDEs
Full Text: DOI
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