Lyapunov Stability of Planar Waves to the Reaction-Diffusion Equation with a Non-Lipschitzian Reaction Term

Figure 2

The subsolutions (red) and supersolutions (green) given in (62)–(63) by a modification of the planar wave (yellow) in . If the initial data is close enough to so that is between sub- and supersolutions at , the solution stays between them for all . The fact that both and are trapped by the sub- and supersolutions whose difference is sufficiently small for all time guarantees the stability of .

(a)

(b)