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Waves
| Speaker: |
Peter Romea Nyarko
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| Date: |
Wednesday September 23, 2009
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| Title: |
Waves and First Order Equations
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Abstract
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We study first order wave equations
which are a class of hyperbolic equations. First we focus on linear
equations, their solution and characteristics. Then we study the method
of characteristics in finding a solution for the nonlinear equations.
Several models for the flux are discussed.
We introduce the integral form of the conservation law and the concept
of discontinuity (shock), moreover we discuss the Rankine-Hugoniot jump
condition. An example of a traffic model that shows the behavior
of cars on a highway is discussed.
Finally we discus weak solution and entropy condition to determine the
unique solution of our nonlinear wave equation.
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