D. E. Panayotounakos, "A new technique in constructing closed-form solutions for nonlinear PDE
A new technique in constructing closed-form solutions for nonlinear PDE
s appearing in fluid mechanics and gas dynamics
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.
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