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A numerical model based on the boundary element method is proposed for the sloshing of a flowing liquid in a three-dimensional tank. Assuming a mean flow in the tank in addition to a perturbation flow, the nonlinear boundary conditions of the liquid free-surface are linearized. Using the boundary element method along with the modal analysis technique a reduced order model is obtained which is used to calculate the fundamental sloshing frequencies and modes in the tank with an inlet and outlet. The obtained results for a test case are compared with the literature data to validate the proposed model. The results are in a very good agreement with analytical results and show an acceptable... 

This paper deals with the blow-up phenomena for a system of parabolic equations with nonlinear boundary conditions. We show that under some conditions on the nonlinearities, blow-up occurs at some finite time. We also obtain upper and lower bounds for the blow-up time when blow-up occurs. Copyright