We consider the nonlinear Poisson equation $$-\Delta u = f(u)$$ in domains $$\Omega \subset {\mathbb {R}}^n$$ with Dirichlet boundary conditions on $$\partial \Omega $$ . show (for monotonically increasing concave f small Lipschitz constant) that if $$D^2 u$$ is negative semi-definite boundary, then concave. A conjecture of Saint Venant from 1856 (proven by Polya 1948) among all fixed measure, ...

The article analyzes the dynamics of channel processes in irrigation pumping station inlet channels. field studies hydraulic and alluvial sediment regimes supply channels stations are analyzed summarized. water flow under conditions extremely high turbidity variability morphometric characteristics presented. which Saint-Venant equations satisfactorily describe flows bed given. Saint-Venant's tw...