Almost Global Existence for Some Semilinear Wave Equations

Our results and approach are related to previous work in the non-obstacle case. In particular, in [2], almost global existence was shown for general, quadratic quasilinear wave equations in Minkowski space, using fully the invariance properties of the wave operator under translations, spatial rotations, scaling, and Lorentz boosts . Subsequently, in [5], the almost global existence of certain divergence-form quadratic quasilinear wave equations was established in Minkowski space, using only the invariance of the wave operator under translations, spatial rotations, and changes of scale. Further techniques and results concerning equations from the theory of elasticity were presented in [9], [10].