Green functions for the heat and Laplace equations with dynamical boundary conditions in a ball
Analysis of PDEs
2025-11-11 v3
Abstract
The green functions for the heat and Laplace equations with dynamical boundary conditions in a ball are studied. First, the green functions of the Laplace equation with a dynamical boundary condition are given, and the properties of related heat kernels are discussed. Then using these ingredients, two complementary approximations to the heat equation with a dynamical boundary condition in a ball are constructed, including an approximation of green function and an approximation of solution. Moreover, the green function of the heat equation with a dynamical boundary condition is implicitly presented by a series of eigenfunctions.
Keywords
Cite
@article{arxiv.2503.09413,
title = {Green functions for the heat and Laplace equations with dynamical boundary conditions in a ball},
author = {Xuzhou Yang},
journal= {arXiv preprint arXiv:2503.09413},
year = {2025}
}
Comments
24pages