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Jerry Bona

2010-05-13
15:30:00 - 16:20:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this pair of lectures, we consider some non-linear, dispersive evolution equations and interest here is in the relationship between solutions posed on bounded and unbounded spatial domains. Such questions have their origins in numerical simulations of problems that arise naturally posed on a half line or on the entire real axis. Problems on the half line come up in modeling laboratory experiments and in the use of nonlinear, dispersive wave equations to address coastal engineering problems. Initial-value problems posed on the entire real axis are often used when one considers disturbances far from the lateral boundaries. Numerical simulation of such problems inevitably relies upon posing the evolution equation on a bounded domain with suitable Dirichlet, Neumann or periodic boundary conditions. To analyze how well numerical simulations approximate the idealized world, one needs comparisons between the solutions of the partial differential equations posed on bounded and unbounded domains. It is to these issues that the lectures devolve after the genesis of the problems is explained. Explicit, and reasonably sharp estimates of the difference between solutions posed on bounded and on unbounded domains are one of the major outcomes of our analysis.