Solvability of the heat equation on a half-space with a dynamical boundary condition and unbounded initial data
Analysis of PDEs
2023-07-05 v1
Abstract
We study the linear heat equation on a halfspace with a linear dynamical boundary condition. We are interested in an appropriate choice of the function space of initial functions such that the problem possesses a solution. It was known before that bounded initial data guarantee solvability. Here we extend that result by showing that data from a weighted Lebesgue space will also do so.
Keywords
Cite
@article{arxiv.2210.14654,
title = {Solvability of the heat equation on a half-space with a dynamical boundary condition and unbounded initial data},
author = {Marek Fila and Kazuhiro Ishige and Tatsuki Kawakami},
journal= {arXiv preprint arXiv:2210.14654},
year = {2023}
}