The Mathematical Biology and Dynamical Systems Seminar series presents Ohio University alum Dr. Muhammad Usman discussing “Theory and Computation: Forced Oscillations of a Class of Shallow Water Wave Equation” on Tuesday, April 3, from 3:05 to 4 p.m. in Morton 326.
Dr. Muhammad Usman
Usman is Associate Professor of Mathematics at the University of Dayton. He obtained a master’s degree in Mathematics (2000) and in biophysics (2001) from Ohio University, followed by a master’s degree in Nuclear and Radiological Engineering and a Ph.D. in Mathematics from the University of Cincinnati (2007).
ABSTRACT: In this talk, I will present the eventual periodicity of the initial boundary value problem (IBVP) for the Korteweg-de Vries (KdV) type equation posed on a bounded domain. It is shown that if the boundary forcing is periodic of period T , then the solution u of the IBVP at each spatial point becomes eventually periodic of period T. I will also exhibit the numerical eventual periodicity using a collocation method. A brief history of this remarkable nonlinear partial differential equation will also be discussed. KdV equation has a very interesting history since the discovery of solitary wave by Scott Russell. KdV equations has many applications in electro optics, medicine, and theoretical physics.
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