Decay of mass for a semilinear heat equation on Heisenberg group

2025/04/21 by Fino, Ahmad Z.
#35A01 #35B33 #35B40 #35K57 #35R03 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.14998

Abstract

In this paper, we are concerned with the Cauchy problem for the reaction-diffusion equation with time-dependent absorption u_t-Δ_ℍu=- k(t)u^p posed on ℍⁿ, driven by the Heisenberg Laplacian and supplemented with a nonnegative integrable initial data, where p>1, n≥ 1, and k:(0,∞)→(0,∞) 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≤ 1+2/Q, while the classical/anomalous diffusion effects win if p>1+2/Q, where Q=2n+2 is the homogeneous dimension of ℍⁿ.

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