Blowup of small data solutions for a class of quasilinear wave equations in two dimensions: An outline of the proof. (English) Zbl 0896.35087

Colombini, Ferruccio (ed.) et al., Geometrical optics and related topics. Selected papers of the meeting, Cortona, Italy, September 1996. Boston, MA: Birkhäuser. Prog. Nonlinear Differ. Equ. Appl. 32, 1-15 (1997).
The author studies the time of existence of smooth solutions for a nonlinear wave equation with velocity of propagation depending on the first-order derivatives. For a special class of this type of equation, he shows that Hörmander gives the precise asymptotic lifespan of the solutions.
For the entire collection see [Zbl 0878.00061].


35L70 Second-order nonlinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs