Decay rates to equilibrium in a nonlinear subdiffusion equation with two counteracting terms

Abstract

In this paper we prove convergence to a steady state as $t\to \infty$ for solutions to the subdiffusion equation \[ \partial_t^αu - \mathbb{L} u = q(x)u - p(x)f(u) + r \] with the exponential ($\hat{I}\pm =1$) or power law ($\hat{I}\pm \in [0,1)$) rates under mild conditions on the coefficients $p$, $q$, the nonlinearity $f$, the source $r$, and the elliptic operator $\mathbb{L}$.