- #1
NeoDevin
- 334
- 2
I need a little help solving an equation here, I don't really know where to start. If anyone has any advice on solving (or even simplifying) such a beast, it would be much appreciated.
\frac{\partial}{\partial t}N + \frac{1}{\tau}N = -a(t)\frac{\partial}{\partial u}N - u\frac{\partial}{\partial x}N -v\frac{\partial}{\partial y}N + \frac{1}{\tau}D(u,v)\int_{-\infty}^\infty\int_{-\infty}^\infty Ndudv
Where
N = N(u,v,x,y,t)
D(u,v) Is a given normalized distribution function. I get to choose this, if you need a particular example, use:
D(u,v) = \frac{1}{2\pi v_{th}^2}e^{-(u^2+v^2)/2v_{th}^2}
a(t) = A_0\cos(\omega t)
A_0, v_{th}, and \tau are all positive real constants.
And the solution N must be normalizable over u and v
\frac{\partial}{\partial t}N + \frac{1}{\tau}N = -a(t)\frac{\partial}{\partial u}N - u\frac{\partial}{\partial x}N -v\frac{\partial}{\partial y}N + \frac{1}{\tau}D(u,v)\int_{-\infty}^\infty\int_{-\infty}^\infty Ndudv
Where
N = N(u,v,x,y,t)
D(u,v) Is a given normalized distribution function. I get to choose this, if you need a particular example, use:
D(u,v) = \frac{1}{2\pi v_{th}^2}e^{-(u^2+v^2)/2v_{th}^2}
a(t) = A_0\cos(\omega t)
A_0, v_{th}, and \tau are all positive real constants.
And the solution N must be normalizable over u and v
