Front Propagation in the Reaction-Telegraph Equation

In this section we consider the problem of front propagation for the three-dimensional reaction-telegraph equation involving KPP kinetics. The goal is to derive the equation governing the evolution of the front in the long-time large-scale limit as in the previous sections and to show that this equation is identical in form to the relativistic Hamilton-Jacobi equation. 

Consider the reaction-telegraph equation (2.19) in three dimensions. 

The limiting function G t, jc) obeys the first-order nonlinear PDE  

The basic idea is that equation (5.50) is identical in form to an equation arising in classical relativity theory. If we introduce the new parameters 

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