jbusc
Oct25-06, 06:34 PM
Hi,
when solving PDE's of the form au_{xx} + 2bu_{xy} + cu_{yy} = 0 where ac - b^2 = 0 (i.e., parabolic)
is the solution always of the form:
u = xf_1 (\phi) + f_2(\phi)
where
\phi is the solution to the characteristic equation a(y')^2 -2by' + c = 0
If not, is there a general form in this sense? (Related to the heat equation in the same way that d'Alembert's form relates to the wave equation)
Thanks, any help at all please is welcome.
when solving PDE's of the form au_{xx} + 2bu_{xy} + cu_{yy} = 0 where ac - b^2 = 0 (i.e., parabolic)
is the solution always of the form:
u = xf_1 (\phi) + f_2(\phi)
where
\phi is the solution to the characteristic equation a(y')^2 -2by' + c = 0
If not, is there a general form in this sense? (Related to the heat equation in the same way that d'Alembert's form relates to the wave equation)
Thanks, any help at all please is welcome.