THE MONOTONICITY PROPERTIES OF THE SOLUTIONS OF FIRST-ORDER ELLIPTIC-SYSTEMS AND THEIR APPLICATIONS TO THE EQUATIONS OF FLUID AND GAS MECHANICS

It is shown that the solution of a homogeneous quasilinear elliptic sy stem of two equations has a monotonicity property, according to which each of the two functions considered varies monotonically along the le vel line of the other function. A connection between the monotonicity property and the extremal properties of the solutions of the systems c onsidered is pointed out. An algorithm for converting certain inhomoge neous and, in particular, homogeneous systems into homogeneous ones is proposed, which considerably extends the amount of information on the monotonicity properties and on the extremal properties of the solutio ns. The value of the results obtained is demonstrated using the exampl e of the axisymmetric and plane flow of an incompressible fluid and a gas.