On the application of the Cole–Hopf transformation to hyperbolic equations based on second-sound models

P.M. Jordan

Mathematics and Computers in Simulation (MATCOM), 2010, vol. 81, issue 1, 18-25

Abstract: We point out and examine two nonlinear, hyperbolic equations, both of which arise in kinematic-wave theory, that can be solved exactly using a conditional application of the Cole–Hopf transformation. Both of these equations are based on flux relations that were originally proposed as models of thermal wave phenomena, also known as second-sound. We then show how this method can be extended and used to obtain a particular type of exact solution to a class of nonlinear, hyperbolic PDEs.

Keywords: Hyperbolic Burgers’ equation; Cole–Hopf transformation; Kinematic-wave theory; Traveling waves (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2010:i:1:p:18-25

DOI: 10.1016/j.matcom.2010.06.011

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