An Optimal Decay Estimation of the Solution to the Airy Equation

Ms. Ashley Scherf
University of Wisconsin-Milwaukee
Graduate Student

In this thesis we investigate the initial value problem to the Airy equation

∂_tu + ∂³_xu = 0, (1)
u(0, x) = f(x).  (2)

We found the optimal decay estimate of the solution to the initial value problem
(1)-(2). The main tool we used is Fourier analysis and oscillatory integrals.

Committee Members:
Profs. Lijing Sun (advisor), Chao Zhu, and Gabriella Pinter