Uniqueness of solution for a nonlinear heterogeneous evolution dam problem
Messaouda Ben Attia, Elmehdi Zaouche, Mahmoud Bousselsal
TL;DR
This paper proves the uniqueness of solutions for a nonlinear evolution dam problem in heterogeneous porous media using advanced mathematical techniques, ensuring the model's reliability in complex geological settings.
Contribution
It introduces a novel proof of solution uniqueness for nonlinear evolution dam problems in arbitrary heterogeneous media, expanding theoretical understanding.
Findings
Established the uniqueness of solutions in heterogeneous media.
Applied the method of doubling variables to nonlinear problems.
Provided a rigorous mathematical framework for dam problem analysis.
Abstract
By choosing convenient test functions and using the method of doubling variables, we prove the uniqueness of the solution to a nonlinear evolution dam problem in an arbitrary heterogeneous porous medium of IR^n with an impermeable horizontal bottom.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Navier-Stokes equation solutions · Advanced Numerical Methods in Computational Mathematics