Local solution of a mixed problem for a degenerated hyperbolic equation (Q1207351)

The author proves the existence of a local solution for the mixed problem associated with the equation \[ u''+(1+M_ 0(| A^{1/2} u|^ 2))Au+M_ 1(| A^{1/2} u|^ 2)Au''=0, \] where \(A\) is a selfadjoint operator defined in a Hilbert space, \(M_ 0,M_ 1\in C\langle 0,\infty)\) are real nonnegative functions and \(| M_ 1'(\sigma)\sigma\mid| \leq CM_ 1(\sigma)\). The proof makes use of the penalty method combined with the Galerkin method and compactness arguments.