Asymptotic profiles for inhomogeneous heat equations with memory

Carmen Cortázar; Fernando Quirós; Noemí Wolanski

Asymptotic profiles for inhomogeneous heat equations with memory

Analysis of PDEs 2023-02-22 v1

Authors: Carmen Cortázar , Fernando Quirós , Noemí Wolanski

Abstract

We study the large-time behavior 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 dimension is large, $N> 4\beta$ . The asymptotic profiles depend strongly on the space-time scale and on the time behavior of the spatial $L^1$ norm of the forcing term.

Keywords

inhomogeneous heat equation memory kernel caputo derivative asymptotic profile large-time behavior lp norms

Cite

@article{arxiv.2302.10251,
  title  = {Asymptotic profiles for inhomogeneous heat equations with memory},
  author = {Carmen Cortázar and Fernando Quirós and Noemí Wolanski},
  journal= {arXiv preprint arXiv:2302.10251},
  year   = {2023}
}

Comments

29 pages

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