Hello, I have some trouble seeing why the solution of the wave equation in 2 dimensions exist at all later times once it passes an initial disturbance....(adsbygoogle = window.adsbygoogle || []).push({});

For example, take a simple case where the initial position is zero, and the initial velocity equals some function inside some circle domain. The solution would be:

[tex]\frac{1}{2\pi }\int \int \frac{\psi (x,y)\partial x\partial y}{\sqrt{t_{o}^{2}-(x-x_{0})^{2}-(y-y_{o})^{2}}}[/tex]

1) Where in that equation tells you that the solutions continues to exist at all later times?

2) If the initial velocity was zero outside the circle domain, why would the solution continue to exist? If we plug in Ψ = 0, wouldn't the solution be zero instead?

3) Can a solution be negative?

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

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

# Domain of influence for wave equation in 2 dimensions

Loading...

Similar Threads - Domain influence wave | Date |
---|---|

A Heat equation on infinite domain | Jan 19, 2018 |

A Laplace equation- variable domain | Sep 21, 2017 |

A Convert to frequency domain | Mar 14, 2017 |

A Laplace equation on a trapezoid | Nov 13, 2015 |

Question on the influence of inconsistent initial values on solving periodic IVP | Nov 11, 2011 |

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