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

Barbara Kaltenbacher

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arXiv · 2601.21038

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

Barbara Kaltenbacher

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Abstract

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

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Barbara Kaltenbacher. 2026-01-28. Decay rates to equilibrium in a nonlinear subdiffusion equation with two counteracting terms. https://arxiv.org/abs/2601.21038

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