On the uniqueness of the limit for an asymptotically autonomous semilinear equation on Rⁿ

Original · EN

We consider a parabolic equation of the form uₜ=Δu +f(u)+h(x,t) in Rⁿ× (0,∞), where f in C¹(R) is such that f(0)=0 and f'(0)<0 and h is a suitable function on Rⁿ× (0,∞). We show that under certain conditions, each globally defined and nonnegative bounded solution u converges to a single steady state.