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

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 ($α=1$) or power law ($α\in[0,1)$) rates under mild conditions on the coefficients $p$, $q$, the nonlinearity $f$, the source $r$, and the elliptic operator $\mathbb{L}$.

💡 Research Summary

The paper investigates the long‑time behavior of solutions to a nonlinear subdiffusion equation that incorporates a fractional time derivative of order α∈