Type of Thesis
In general, existence of solutions to nonlinear wave equations heavily depends on the nonlinearity. The publication by Howard et al. proves global existence of solutions to wave equations with nonlinear damping and power source terms. However, the nonlinear damping can also act as a source term when the sign of the term is switched. In this paper, we prove local existence under linear damping combined with a nonlinear damping term. We also show that solutions which exist for only finite time must blow up. We prove this via fixed point iteration methods on Sobolev spaces.
Richman, Justin, "Well-Posedness of the Damped Wave Equation with Nonlinear Source Terms" (2018). Undergraduate Honors Theses. 1688.