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On the Existence of Global Weak Solutions to 1D Sediment Transport Model

This paper is devoted to the study of the existence of weak solution in time with a periodic domain of sediment transport model. We consider a one-dimensional viscous sediment transport model which combines a viscous Shallow-Water system with a transport equation that describes the bottom evolution. The model studied does not take into account all the regularizing terms used by Roamba Brahima, Zongo Yacouba and Jean de Dieu Zabsonre (2017) and we use a better transport equation than that used by Zabsonre (2012).