- #1

jbusc

- 211

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Hi,

when solving PDE's of the form [tex]au_{xx} + 2bu_{xy} + cu_{yy} = 0[/tex] where [tex]ac - b^2 = 0[/tex] (i.e., parabolic)

is the solution always of the form:

[tex]u = xf_1 (\phi) + f_2(\phi) [/tex]

where

[tex] \phi[/tex] is the solution to the characteristic equation [tex] a(y')^2 -2by' + c = 0[/tex]

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 [tex]au_{xx} + 2bu_{xy} + cu_{yy} = 0[/tex] where [tex]ac - b^2 = 0[/tex] (i.e., parabolic)

is the solution always of the form:

[tex]u = xf_1 (\phi) + f_2(\phi) [/tex]

where

[tex] \phi[/tex] is the solution to the characteristic equation [tex] a(y')^2 -2by' + c = 0[/tex]

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.

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