标题： 一维非线性扩散方程在Lp Lq最大正则性设置下的动态和第四类边界条件的柯西问题适定性 显示英文标题

标题： Well-Posedness of the Cauchy Problem for One-Dimensional Nonlinear Diffusion Equations with Dynamic and Fourth-Type Boundary Conditions in the Lp Lq Maximal Regularity Setting

摘要： 本文研究了带有动态边界条件和一个使一维拉普拉斯算子自伴的附加边界条件的一维扩散方程的柯西问题的局部适定性。 该方程用于描述水族箱中的过滤过程，最初由作者和Kitahata提出。 本文处理的边界条件不同于经典的狄利克雷、诺伊曼和罗宾条件；我们将其称为第四种或FK型边界条件。 该边界条件旨在捕捉过滤过程中两个边界之间的相互作用。 建立适定性的框架基于L^p-L^q最大正则性类。 显示英文摘要

摘要： This paper addresses the local well-posedness of the Cauchy problem for a one-dimensional diffusion equation equipped with a dynamic boundary condition and an additional boundary condition that renders the one-dimensional Laplace operator self-adjoint. The equation serves as a model for describing filtration in aquaria, originally introduced by the author and Kitahata. The boundary condition treated in this work differs from classical types such as Dirichlet, Neumann, and Robin conditions; we refer to it as the fourth or FK-type boundary condition. The boundary condition is designed to capture interactions between the two boundaries in the context of filtration. The framework for establishing well-posedness is based on L^p-L^q maximal regularity classes.