Equations des ondes semi-linéaires. II: Contrôle des singularités et caustiques non linéaires. (Semilinear wave equations. II: Control of nonlinear singularities and caustics). (French) Zbl 0686.35015

Lebeau, G.

Invent. Math. 95, No. 2, 277-323 (1989).

[See also the following review.]
If u(x,t) is a solution of the semilinear wave equation \(\square u=P(t,x,u)\) in \({\mathbb{R}}^{d+1}\), which belongs to \(C_ 0({\mathbb{R}}_ t;H^ s)\), \(s>d/s\), and with Cauchy data conormal with respect to some analytic hypersurface, one study the wave front set of u. In particular, one obtains the location of the singularities in the case of the swallowtail caustic.

Reviewer: G.Lebeau

MSC:

35B40	Asymptotic behavior of solutions to PDEs
35L70	Second-order nonlinear hyperbolic equations
35L15	Initial value problems for second-order hyperbolic equations

Keywords:

semilinear wave equations; singularities; wave front set

Citations:

Zbl 0686.35016

References:

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