Ben Preskill
Harvey Mudd College Mathematics 2009
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| Thesis Proposal: | Generalized Criteria for No Continuous Solution of a Semilinear Wave Equation |
|---|---|
| Thesis Advisor: | Prof. Alfonso Castro |
| Second Reader: | Prof. Adolfo Rumbos |
| E-Mail: | bpreskill@math.hmc.edu |
Existence and Nonexistence of Continuous Solutions to a Semilinear Wave Equation
We prove two results; first, we show that a boundary value problem for the smilinear wave equation with smooth, asymptotically linear nonlinearity and sinusoidal smooth forcing along a characteristic cannot have a continuous solution. Thereafter, we show that if the sinudoidal forcing is not isolated to a characteristic of the wave equation, then the problem has a continuous solution.
Thesis: Existence and Nonexistence of Continuous Solutions to a Semilinear Wave Equation