Generic hyperbolicity for the equilibria of the one-dimensional parabolic equation\newline \(u_t=(a(x)u_x)+f(u)\) (Q1879174)

This work is a continuation of the one published by the same author in [Proc. R. Soc. Edinb., Sect. A 123, No. 6, 1031--1040 (1993; Zbl 0832.35051)]. There, he stablished generic hyperbolicity for the same type of problem with respect to \(a\) and \(f\) if additional hypotheses were imposed on the equation. Here, he eliminates those additional requirements on the equilibria but at the price of imposing new ones on \(a\).