生物膜生长的双曲-抛物型自由边界问题的解的存在性与唯一性
偏微分方程分析
2025-03-26 v2
摘要
本文关于与生物膜生长相关的自由边界值问题的解的存在性与唯一性。该问题包含若干非线性双曲型偏微分方程组，描述微生物种群的生长；以及描述基质动力学的抛物型偏微分方程组。自由边界的演化由一个常微分方程描述，考虑生物膜的厚度。我们采用特征法和固定点策略来证明在小时及所有时间上的存在性与唯一性定理。所有方程均被转化为积分方程，特别是通过利用Green's函数将抛物型方程进行此转换。我们考虑基质方程的Dirichlet-Neumann和Neumann-Robin边界条件及其可变情况的延伸。
引用
@article{arxiv.2411.17974,
title = {Existence and uniqueness of solution to a hyperbolic-parabolic free boundary problem for biofilm growth},
author = {Dieudonné Zirhumanana Balike and Luigi Frunzo and Maria Rosaria Mattei and Fabiana Russo},
journal= {arXiv preprint arXiv:2411.17974},
year = {2025}
}
备注
We kindly request the withdrawal of our submission due to a misunderstanding among the co-authors regarding the decision to upload the work to arXiv. Not all authors had agreed to its public release, and the submission was made based on an internal miscommunication. We regret this oversight and appreciate your assistance in addressing this matter