De. Panayotounakos et D. Drikakis, ON THE CLOSED-FORM SOLUTIONS OF THE WAVE, DIFFUSION AND BURGERS EQUATIONS IN FLUID-MECHANICS, Zeitschrift fur angewandte Mathematik und Mechanik, 75(6), 1995, pp. 437-447
In this paper the closed-form solutions of the first-order wave equati
on with source terms u(t) + g(u)u(x) = f(u), and of the diffusion equa
tion of the general form u(t) + g(u)u(x) = vu(xx), are constructed. Bo
th equations are considered for smooth initial and boundary conditions
, namely u(0, x) = phi(x) and u(t, x(0)) = f(t), respectively. Further
more, the case of Burgers equation with source terms u(t) + uu(x) = vu
(xx) - lambda u, appearing in the aerodynamic theory, is investigated.
The developed solution techniques and the obtained closed-form soluti
ons may be proved powerful in applications.