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arXiv · 2204.11342

Decay/growth rates for inhomogeneous heat equations with memory. The case of small dimensions

Carmen Cortázar·Fernando Quirós·Noemí Wolanski
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Abstract

We study the decay/growth rates in all $L^p$ norms of solutions to an inhomogeneous nonlocal heat equation in $\mathbb{R}^N$ involving a Caputo $\alpha$-time derivative and a power $\beta$ of the Laplacian when the spatial dimension is small, $1\le N\le 4\beta$, thus completing the already available results for large spatial dimensions. Rates depend not only on $p$, but also on the space-time scale and on the time behavior of the spatial $L^1$ norm of the forcing term.

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Carmen Cortázar, Fernando Quirós, Noemí Wolanski. 2022-04-24. Decay/growth rates for inhomogeneous heat equations with memory. The case of small dimensions. https://arxiv.org/abs/2204.11342

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