Reaction–diffusion on a time-dependent interval: Refining the notion of ‘critical length’

A reaction-diffusion equation is studied in a time-dependent interval whose length varies with time. The reaction term either linear or of KPP type. On fixed interval, it well-known that if the less than certain critical value then solution tends to zero. When domain may vary time, we prove conditions under which does and not converge zero long We show that, even always strictly 'critical length', outcome occur. Examples are given. proof based on upper lower estimates for solution, derived this paper general interval.