The existence and non-existence of travelling front in high order auto-catalysis chemical reaction (Q1933954)

This paper is concerned with the existence and non-existence of travelling waves in a high order auto-catalysis chemical reaction. The previous work [\textit{X. Chen} and the first author, SIAM J. Math. Anal. 39, No. 2, 437--448 (2007; Zbl 1360.34065)] made a progress on this problem, especially when the auto-catalysis moves faster than the reactant. Among other results, this paper gives more accurate bounds for the admissible/non-admissible speeds of traveling waves when the auto-catalysis moves slower than the reactant and the reaction relation is high.