On the Uniqueness of the Limit for an Asymptotically Autonomous Semilinear Equation on ℝN
Carmen Cortázar, Marta García‐Huidobro, Pilar Herreros · Communications in Partial Differential Equations · 2015
We consider a parabolic equation of the form where f ∈ C 1(ℝ) is such that f(0) = 0 and f′(0) <0 and h is a suitable function on ℝ N × (0, ∞). We show that, under certain assumptions on f and u, each globally defined and nonnegative bounded solution u converges to a single steady state.