MATHEMATICAL ANALYSIS OF FLOOD DYNAMICS AT THE BRANCH OF THE GRAND BALÉ IN THE LOCALITY OF HÈRÈDOUGOU IN BURKINA FASO

This article focuses on a two-dimensional Saint-Venant problem that we proposed for modeling flooding phenomena occurring in the locality of Hèrèdougou in Burkina Faso. The classic solution to this problem is very delicate due to the possible formation of discontinuities. We therefore adopt the concept of weak entropy solutions in order to ensure the physical relevance of the solution and its uniqueness. The existence results of the solution to the weak problem are established using the regularization method of the original system, combined with uniform a priori estimates and compactness arguments; which ensures the convergence to a weak solution. Uniqueness is achieved through energy inequalities that exploit the Grönwall’s lemma. Under suitable assumptions on the initial data and boundary conditions, we establish that the proposed mathematical model admits a unique weak entropy solution.