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Zbl 0615.35053
Rauch, J.; Reed, M.
Classical, conormal, semilinear waves. (English)
[J] Sémin., Équations Dériv. Partielles 1985-1986, Exposé No.5, 17 p. (1986).

We discuss, in more detail, the conormal progressing waves constructed by {\it J. M. Bony} [Semin. Goulaouic-Meyer-Schwartz, Equations Deriv. Partielles 1981-1982, Expose No.2, 11 p. (1982; Zbl 0498.35017)]. The goal is to show that if the wave ($\equiv$ solution) is classical in the past, it remains so in the future. Given a certain minimal regularity this is true provided the notion of classicality is slightly extended so as to yield a class closed under nonlinear functions.

MSC 2000:: *35L60 First-order nonlinear hyperbolic equations
35Q99 PDE of mathematical physics and other areas
35B65 Smoothness of solutions of PDE
35B40 Asymptotic behavior of solutions of PDE
46E35 Sobolev spaces and generalizations

Keywords: Besov space; conormal progressing waves; minimal regularity; classicality

Citations: Zbl 0498.35017

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