具有混合边界条件的非线性Boussinesq地下水流动模型的弱可解性：Moche CHAVIMOCHIC含水层

中文摘要 AI 辅助

我们证明了由秘鲁北部Moche CHAVIMOCHIC含水层所启发的二维非线性Boussinesq型地下水流动问题的弱可解性。该模型将依赖于状态的储水系数和导水系数与由水文地质几何决定的边界分解（包括Dirichlet、Neumann和非线性Robin部分）耦合在一起。与地下水Boussinesq文献中许多致力于针对特殊几何和边界数据的精确解、相似解、微扰解、半解析解或线性化解的研究不同，我们的目标是对一个真正的二维混合边界问题建立变分存在性结果。由于物理导水系数与饱和厚度成正比，方程在局部枯竭时退化。因此，我们隔离出一个物理上可接受的饱和范围，并构造本构定律的一致正延拓。对于由此产生的均匀抛物型问题，我们通过隐式Euler Rothe格式、适应储水规律的非线性能量、离散导数的一致估计、离散紧致性以及边界迹的强收敛性，获得了弱解的存在性。随后，我们给出了一个精确的一致性陈述，说明抽象解何时能求解原始Moche模型，并将完全枯竭区域识别为一个独立的孔隙介质型问题。

英文摘要

We prove weak solvability for a two dimensional nonlinear Boussinesq type groundwaterflow problem motivated by the Moche CHAVIMOCHIC aquifer in northern Peru. The model couples state dependent storage and transmissivity with a boundary decomposition into Dirichlet, Neumann, and nonlinear Robin parts dictated by the hydrogeological geometry. In contrast with much of the groundwater Boussinesq literature, which is devoted to exact, similarity, perturbative, semi-analytical, or linearized solutions for special geometries and boundary data, our objective is a variational existence result for a genuinely two-dimensional mixed-boundary problem. Because the physical transmissivity is proportional to the saturated thickness, the equation degenerates at local depletion. We therefore isolate a physically admissible saturated range and construct uniformly positive extensions of the constitutive laws. For the resulting uniformly parabolic problem, existence of a weak solution is obtained through an implicit Euler Rothe scheme, a nonlinear energy adapted to the storage law, uniform estimates for the discrete derivative of the storage potential, discrete compactness, and strong convergence of boundary traces. We then give a precise consistency statement showing when the abstract solution solves the original Moche model and identify the fully depleted regime as a distinct porous medium type problem.

发表机构

• Universidad Nacional de Trujillo（特鲁希略国立大学）
• Universidade Federal da Integração Latino-Americana (UNILA)（拉丁美洲一体化联邦大学）

机构由 AI 辅助整理，请以论文原文为准。