Extension of the segregative pulsating fronts exclusivity theorem to non-constant extinction states

The paper considers the non-constant case of the extinction states appearing in the segregative pulsating-front problem. The preceding proof establishes the result only when the relevant coefficients are constant, because the needed $L^\infty$ estimates fail for non-constant extinction states.

Segregative pulsating fronts exclusivity conjecture. Theorem still holds true in the non-constant case.

The authors state that they do not know how to prove this extension, and describe it as a natural conjecture because the constant-case exclusivity result is expected to persist for non-constant extinction states.