Cauchy problem for a model of nonlinear waves generated in viscous films

This work studies a two‐dimensional version of the Korteweg–de Vries equation, which is the so‐called anisotropic dissipation‐modified Boussinesq–Korteweg–de Vries equation. The local well‐posedness for the Cauchy problem associated with this equation is proven when the initial value belongs to the Sobolev space , for all s > ? 1 ∕ 6. A global existence result will be obtained under suitable conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

An efficient and clean one‐pot synthesis of 3,4‐dihydropyrimidine‐2(1H)‐ones catalyzed by tungstate sulfuric acid in solvent‐free conditions

Tungstate sulfuric acid catalyzes the three component condensation reaction of an aromatic aldehyde, urea and a β‐ketoester under solvent‐free conditions to afford the corresponding dihydropyrimidinones in high to excellent yields at room temperature.