Approximate traveling waves in linear reaction-hyperbolic equations. (English) Zbl 0704.35087
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 \(\infty\), 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.
Reviewer: M.C.Reed
MSC:
35L45 | Initial value problems for first-order hyperbolic systems |
92C30 | Physiology (general) |
35B99 | Qualitative properties of solutions to partial differential equations |
35B25 | Singular perturbations in context of PDEs |