Mathematical Problems in Engineering
Volume 2 (1996), Issue 4, Pages 301-318

A new technique in constructing closed-form solutions for nonlinear PDEs appearing in fluid mechanics and gas dynamics

D. E. Panayotounakos

Dept. of Eng. Science, Sect. of Mech., Nat. Techn. Univ. Athens, 5 Heroes of Polytechnion Avenue, GR-157 73, Zographou, Athens, Hellas, Greece

Received 15 September 1995

Copyright © 1996 D. E. Panayotounakos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We develop a new unique technique in constructing closed-form solutions for several nonlinear partial differential systems appearing in fluid mechanics and gas dynamics. The obtained solutions include fewer arbitrary functions than needed for general solutions, fact that permits us to specify them according to the initial state, or the geometry, of each specific problem under consideration. In order to apply the before mentioned technique we construct closed-form solutions concerning the gas-dynamic equations with constant pressure, the dynamic equations of an ideal gas in isentropic flow, and the two-dimensional incompressible boundary layer flow.