Hyperbolic equations and classes of infinitely differentiable functions (Q1086746)

The authors consider the solvability in the Mandelbrojt classes \(\epsilon \{M_ h\}\) of the Cauchy problem for hyperbolic equations of the type \(u_{tt}-a(t)u_{xx}=0\), where a(t) is a strictly positive continuous function. Mor precisely, they give an example of a function a(t) for which the Cauchy problem is not well-posed in any class \(\epsilon \{M_ h\}\) containing a non-trivial function with compact support.