Dual variational principles for a class of non-linear partial differential equations

Using the scalar product. (f1,f2)=∫Df1(x,y)f2(x,y)exp[m(x)+n(y)]dx dydual variational principles are formulated for certain second-order non-linear partial differential equations. Application is made to magneto-hydrodynamic pipe flow. © 1983, by Academic Press Inc. (London) Ltd.