A necessary and sufficient condition for the hyperbolicity of second order equations with two independent variables. (English) Zbl 0552.35049

Nishitani, Tatsuo

J. Math. Kyoto Univ. 24, 91-104 (1984).

Let \(L=D^ 2_ t-A(t,x)D^ 2_ x+B(t,x)D_ x+C(t,x)D_ t+R(t,x)\) where it is assumed that the coefficients are real analytic in a neighborhood of the origin in \(R^ 2\). Consider the Cauchy problem \(Lu(t,x)=f(t,x),\) \(D^ j_ tu(t_ 0,x)=u_ j(x).\) The author gives a necessary and sufficient condition in order that the Cauchy problem stated above is \(C^{\infty}\)-well-posed.

Reviewer: N.L.Maria

MSC:

35L15	Initial value problems for second-order hyperbolic equations
35A05	General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

Cauchy problem; well-posed