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Classical, conormal, semilinear waves. (English) Zbl 0615.35053
Sémin., Équations Dériv. Partielles 1985-1986, Exposé No. 5, 17 p. (1986).
We discuss, in more detail, the conormal progressing waves constructed by 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.

35L60 First-order nonlinear hyperbolic equations
35Q99 Partial differential equations of mathematical physics and other areas of application
35B65 Smoothness and regularity of solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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