Hi,(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Method of characteristics

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads for Method characteristics | Date |
---|---|

A Solving forced PDE with method of Characteristics | Apr 26, 2016 |

What is Method of Characteristics? | Aug 17, 2015 |

Method of characteristics and second order PDE. | Jan 19, 2014 |

Parameterization for method of characteristics | Oct 22, 2013 |

Method of Characteristics for Hyperbolic PDE | Apr 16, 2013 |

**Physics Forums - The Fusion of Science and Community**