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math.AP2025
Green functions for the heat and Laplace equations with dynamical boundary conditions in a ball
Xuzhou Yang
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…
math.AP2024
Schauder estimate for the boundary diffusion equaiton
Xuzhou Yang
In this paper, a certain type of linear boundary diffusion equation is studied. Such equation is crucial in the research of a non-linear boundary diffusion problem which was origin…
math.AP2022
Stability of the separable solutions for a nonlinear boundary diffusion problem
Tianling Jin, Jingang Xiong, Xuzhou Yang
In this paper, we study a nonlinear boundary diffusion equation of porous medium type arising from a boundary control problem. We give a complete and sharp characterization of the…