Year: 2025
Type: preprint
Abstract: In this paper, we are concerned with the Cauchy problem for the reaction-diffusion equation with time-dependent absorption $u_{t}-Δ_{\mathbb{H}}u=- k(t)u^p$ posed on $\mathbb{H}^n$, driven by the Heisenberg Laplacian and supplemented with a nonnegative integrable initial data, where $p>1$, $n\geq 1$, and $k:(0,\infty)\to(0,\infty)$ is a locally integrable function. We study the large time behavior of non-negative solutions and show that the nonlinear term determines the large time asymptotic for $p\leq 1+2/Q,$ while the classical/anomalous diffusion effects win if $p>1+{2}/{Q}$, where $Q=2n+2$ is the homogeneous dimension of $\mathbb{H}^n$.
Source: arXiv (Cornell University)
Author: Fino, Ahmad Z.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979289313
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