River silting is one of the increasingly common phenomena in the process of climate change. This phenomenon is the cause of degradation of the banks of rivers and their environments. The causes and origins of river silting are varied and complex.

After having developed the equations which govern the sedimentation of rivers, this article proposes a formulation for the identification of the parameters and the source function of bank’s silting phenomenon. The theoretical study of these equations highlights the existence of shock wave lines near river banks. The use of inner asymptotic expansion around the shock wave lines leads to constructing a discrete forward problem from which an appropriate inverse formulation is derived. Then, a calculation of the gradient of the objective function is provided as well as the equations allowing to calculate the parameters to be identified.

rivers silting process, sedimentation models, inner asymptotic expansion, adjoint and tangent equations, optimality system.

Received: September 7, 2022; Accepted: October 19, 2022; Published: November 5, 2022

How to cite this article: Cyr. S. Ngamouyih Moussata, Mahamat Saleh Daoussa Haggar and Benjamin Mampassi, An inverse formulation for identifying the silting process of river banks, Universal Journal of Mathematics and Mathematical Sciences 17 (2022), 31-45. http://dx.doi.org/10.17654/2277141722010

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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