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

2025/03/12 by Yang, Xuzhou
#35E05 #35J08 #35K20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35K05 #Secondary 35K08

paper · doi:10.48550/arxiv.2503.09413

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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• Feeling boundary by Brownian motion in a ball
• Dirichlet heat kernel for the Laplacian in a ball
• Heat-kernel coefficients of the Laplace operator on the 3-dimensional ball
• Fundamental solution to the heat equation with a dynamical boundary condition
• Green function diagonal for a class of heat equations