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

[tex] \Delta w = \frac{ \partial^{2} w }{x_{1}^{2}} + \frac{ \partial^{2} w }{x_{2}^{2}} [/tex]

and [tex] \nabla = \left(\frac{\partial}{\partial x_{1}},\frac{\partial}{\partial x_{2}}\right) [/tex]

[tex]\int_{\Omega} \nabla v \nabla w d \Omega = \int_{\Gamma} v \frac{\partial w}{\partial n} d \Gamma - \int_{\Omega}v \Delta w d \Omega[/tex]

where [tex] \Gamma [/tex] is the boundary of [tex]\Omega [/tex]

so if I have

[tex] - \int_{\Omega}v \Delta w d \Omega [/tex]

I can apply Green's thm to get

[tex] - \int_{\Omega}v \Delta w d \Omega = \int_{\Omega} \nabla v \nabla w d \Omega - \int_{\Gamma} v \frac{\partial w}{\partial n} d \Gamma [/tex]

But what if I'm starting with

[tex] \int_{\Omega} v \left( \frac{\partial^{2} w }{\partial x_{1}^{2}} + k \frac{\partial^{2} w }{\partial x_{2}^{2}} \right) d \Omega [/tex]

where k is some scalar? I'm thrown off by only one of the dimensions being scaled.

**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!

# Applying Green's Formula in 2D

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Applying Green's Formula | Date |
---|---|

A Applying boundary conditions on an almost spherical body | Feb 15, 2018 |

How do I apply rk4 to a second order pde? | Sep 1, 2014 |

Change ODE system to Polar to apply Poincare-Bendixson | Dec 15, 2012 |

Variation of parameters applied to an ODE | Dec 4, 2012 |

Applying shooting method to 4nd two point value boundary problem | Oct 12, 2012 |

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