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Interaction des singularités pour les équations de Klein-Gordon non linéaires. (Interaction of singularities for nonlinear Klein-Gordon equations). (French) Zbl 0555.35118
Sémin. Goulaouic-Meyer-Schwartz 1983-1984, Équat. dériv. part., Exposé No. 10, 27 p. (1984).
The author considers the nonlinear Klein-Gordon equation $$u_{tt}- u_{xx}-u_{yy}=f(t,x,y,u),$$ the problem is to determine the regularity of solutions u for $$t>0$$ when the singularities of u for $$t<0$$ are given. The cases when the singularities are located in a finite number of hypersurfaces $$\Sigma_ j$$ (i.e., u belongs to $$H^ s$$ near $$\Sigma_ j$$, and to $$H^{s+k}$$ otherwise) are studied in some details. To study the propagation of singularities of solutions the author uses a kind of symbolic calculus, called the operator 2-micro-differentials which is a vector field singular at the origin and tangent to the surfaces bearing the initial singularities.
Reviewer: G.-Z.Tu

##### MSC:
 35Q99 Partial differential equations of mathematical physics and other areas of application 35G25 Initial value problems for nonlinear higher-order PDEs 35A20 Analyticity in context of PDEs
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