Classical, conormal, semilinear waves. (English) Zbl 0615.35053

Rauch, J.; Reed, M.

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.

MSC:

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

Keywords:

Besov space; conormal progressing waves; minimal regularity; classicality

Citations:

Zbl 0498.35017