TY - JOUR
T1 - On the Closed‐Form Solutions of the Wave, Diffusion and Burgers Equations in Fluid Mechanics
AU - Panayotounakos, D. E.
AU - Drikakis, D.
PY - 1995/1/1
Y1 - 1995/1/1
N2 - In this paper the closed‐form solutions of the first‐order wave equation with source terms ut + g(u) ux = f(u), and of the diffusion equation of the general form ut + g(u) ux = vuxx, are constructed. Both equations are considered for smooth initial and boundary conditions, namely w(0, x) = (x); u(0, x) = (x) and u(t, x0) = f(t), respectively. Furthermore, the case, of Burgers equation with source terms u, + uux = vwxx‐‐‐δu, appearing in the aerodynamics theory, is investigated. The developed solution techniques and the obtained closed‐form solutions may he proved powerful in applications.
AB - In this paper the closed‐form solutions of the first‐order wave equation with source terms ut + g(u) ux = f(u), and of the diffusion equation of the general form ut + g(u) ux = vuxx, are constructed. Both equations are considered for smooth initial and boundary conditions, namely w(0, x) = (x); u(0, x) = (x) and u(t, x0) = f(t), respectively. Furthermore, the case, of Burgers equation with source terms u, + uux = vwxx‐‐‐δu, appearing in the aerodynamics theory, is investigated. The developed solution techniques and the obtained closed‐form solutions may he proved powerful in applications.
UR - http://www.scopus.com/inward/record.url?scp=84981816149&partnerID=8YFLogxK
U2 - 10.1002/zamm.19950750604
DO - 10.1002/zamm.19950750604
M3 - Article
AN - SCOPUS:84981816149
SN - 0044-2267
VL - 75
SP - 437
EP - 447
JO - ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
JF - ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
IS - 6
ER -