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Resonantly interacting weakly nonlinear hyperbolic waves. I: A single space variable. (English) Zbl 0572.76066
A systematic asymptotic theory is presented for resonantly interacting weakly nonlinear hyperbolic waves in one space variable. The theory includes as a special case the theory of nonresonant interacting waves for general hyperbolic systems developed recently by J. K. Hunter and J. B. Keller [see e.g.: Commun. Pure Appl. Math. 36, 547-569 (1983; Zbl 0547.35070)], when specialized to one space variable. Here resonances are included. Such resonances are typical when the hyperbolic system has at least three equations and when, for example, small- amplitude periodic initial data are given.

MSC:
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q30 Navier-Stokes equations
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