Green functions for the heat and Laplace equations with dynamical boundary conditions in a ball

Xuzhou Yang

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arXiv · 2503.09413

Green functions for the heat and Laplace equations with dynamical boundary conditions in a ball

Xuzhou Yang

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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.

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Xuzhou Yang. 2025-03-12. Green functions for the heat and Laplace equations with dynamical boundary conditions in a ball. https://arxiv.org/abs/2503.09413

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