A stability analysis for a semilinear parabolic partial differential equation

Abstract

We consider a parabolic partial differential equation u t = u xx + f( u), where − ∞ < x < + ∞ and 0 < t < + ∞. Under suitable hypotheses pertaining to f, we exhibit a class of initial data φ( x), − ∞ < x < + ∞, for which the corresponding solutions u( x, t) approach zero as t → + ∞. This convergence is uniform with respect to x on any compact subinterval of the real axis.