Localized and Expanding Entire Solutions of Reaction–Diffusion Equations

This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions some reaction–diffusion equations in $$\mathbb {R}^N$$ any space dimension N. The are assumed to be localized past. Under certain conditions on reaction term, then proved time-independent or heteroclinic connections between different steady states. Furthermore, either they uniformly time, converge a constant state and spread at large time. result applied specific bistable-type reactions.