APPROXIMATE TRAVELING WAVES IN LINEAR REACTION-HYPERBOLIC EQUATIONS

Linear reaction-hyperbolic equations of a general type arising in certain physiological problems do not have traveling wave solutions, but numerical computations have shown that they possess approximate traveling waves. Using singular perturbation theory, it is shown that as the rates of the chemical reactions approach ∞, solutions approach traveling waves. The speed of the limiting wave and the first term in the asymptotic expansion are computed in terms of the underlying chemical mechanisms.