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