On Necessary and Sufficient Conditions for $L^2$-Well-Posedness of Mixed Problems for Hyperbolic Equations

Caractérisation des problèmes mixtes hyperboliques bien posés

“…Dans cette première partie, our cela, nous allons transformer (3.2) en un problème équivalent sur le bord {x = 0} en adaptant au cas hyperbolique la ^méthode des ^potentiels telle qu'elle'est développée dans [5], [9]. Rappelons tout d'abord la îorinulle de& 1 . satits :…”

$L^2$-well-posedness for Hyperbolic Mixed Problems

“…On the other hand, since fl*/±^j( -7-) ^z-5 we have \ fl/j / Let every real point be regular. In order that (P) is L 2 -well-posed, it is sufficient thatPiJ.lh&i ^) I d~,2~ 2m * di 2 r, 97; fiifo n n (£/~X r > ?…”

$C^∞$ Ill-Posedness of the Mixed Problem for Hyperbolic Equations of Second Order

“…When the coefficients of L and B are all constant and Q=R 1 xR+xR n~1 , we know a necessary and sufficient condition for C°° wellposedness by Sakamoto [5]. In [1], Agemi and Shirota studied the mixed problem for wave equation in a half space precisely when n-2, b z and c are real constants, and f-0.…”