Abstract
Second-order partial differential equations (PDEs) are traditionally classified as being parabolic, elliptic, or hyperbolic in nature, and this classification largely determines the kind of analytical and numerical techniques that can be successfully applied to them. Beyond this there exists a much broader variety of systems and high-order PDEs, with a correspondingly vast range of behaviors and requiring a nearly endless list of distinct techniques for their solution or approximation. Among these classes, systems of first-order hyperbolic PDEs are prominent in physical applications and have a highly-developed theory and corresponding tools for their solution. In this talk I will show how any system of PDEs of any order can be approximated arbitrarily well by a system of first-order hyperbolic PDEs. I will show several examples, focusing mainly on dispersive wave equations, and discuss the advantages and potential weaknesses of this technique.
Brief Biography
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