Collections > Electronic Theses and Dissertations > AN INVESTIGATION OF NON-TRAPPING, ASYMPTOTICALLY EUCLIDEAN WAVE EQUATIONS
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In this dissertation, we demonstrate almost global existence for a class of variable coefficient, non-trapping, asymptotically Euclidean, quasilinear wave equations with small initial data. A novel feature is that the wave operator may be a large perturbation of the usual D'Alembertian operator. The key step is developing a local energy estimate for an appropriately linearized version of our wave equation. The linearized wave operator is a combination of a stationary, non-trapping, asymptotically Euclidean wave operator and a small time-dependent perturbation. The time-dependent perturbation need not be asymptotically Euclidean.