Exact solution structures on some nonlocal overdetermined problems
Analysis of PDEs
2025-12-18 v1
Abstract
In this paper, we study the solution structures of Serrin-type overdetermined problems with Kirchhoff-type nonlocal terms. We prove that the exact number of solutions is the same as those of some transcendental equations defined by the nonlocal terms. We also obtain the explicit form of solutions by using the unique solutions of the overdetermined problems without the nonlocal terms.
Keywords
Cite
@article{arxiv.2512.14987,
title = {Exact solution structures on some nonlocal overdetermined problems},
author = {Kazuki Sato and Futoshi Takahashi},
journal= {arXiv preprint arXiv:2512.14987},
year = {2025}
}
Comments
10 pages, submitted