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arXiv · 2609.38031

Weak solvability of a nonlinear Boussinesq groundwater flow model with mixed boundary conditions: the Moche CHAVIMOCHIC aquifer

Alexis Rodriguez Carranza·Víctor Arturo Martínez León·Alan Chávez Obregón
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Abstract

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.

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Alexis Rodriguez Carranza, Víctor Arturo Martínez León, Alan Chávez Obregón. 2026-09-29. Weak solvability of a nonlinear Boussinesq groundwater flow model with mixed boundary conditions: the Moche CHAVIMOCHIC aquifer. https://arxiv.org/abs/2609.38031

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