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Jianfeng Xia April 7, 2005 13:01

how can solve this equation
 
I have to a equation , but I don't known how to solve it stable.

partial h/partial t= Grad. {1/3 h^3 Grad[-gamma chi(h) Grad. (Grad h/ sqrt(1+(Grad h)^2))+ chi'(h)(gamma 1/sqrt(1+(Grad h)^2))]}

Is there anyone can help me , Thank you very much

Junseok Kim April 8, 2005 14:50

Re: how can solve this equation
 
Could you make it ps or pdf file using latex, so that easy to look at the equation. It is hard to visualize the equation unless I rewrite it again.

You can post it on your website and put the link here.

Kim

Jianfeng Xia April 8, 2005 14:55

Re: how can solve this equation
 
Thanks a lot, But I have no my own website.

Can I set pdf file to your email box?

Junseok Kim April 8, 2005 14:59

Re: how can solve this equation
 
Sure, no problem. And if you don't mind I will put it on my website so that others can look at and give you ideas.

Kim

Jianfeng Xia April 8, 2005 15:02

Re: how can solve this equation
 
OK.


m. malik April 8, 2005 16:02

Re: how can solve this equation
 
Will appreciate if you can e-mail me the equation. Thanks

Junseok Kim April 8, 2005 17:15

http://math.uci.edu/~jskim/web.pdf
 
Here is the problem description.

http://math.uci.edu/~jskim/web.pdf

diaw April 9, 2005 23:28

Re: how can solve this equation
 
Your problem statement describes h(x), ie. a 1D problem.

But, your equation is full of Nabla operators, implying a vector field (2d or 3d), as it seems pointless using nablas for only a 1D problem.

If it is a 1D problem, then the reduction to a simple PDE is straightforward, if h(x,y,z), then the expansion will become more complex... then I would have an issue with the sqr(1+(nabla h )^2) term...

A few thoughts...

In a 1D problem, I would initially be inclined to try a change of variable to allow simpler solution & substitute back as required.

diaw...

???? April 10, 2005 10:31

Re: http://math.uci.edu/~jskim/web.pdf
 
What is h(X) the profile of? What variable?

Jianfeng Xia April 10, 2005 20:26

Re: how can solve this equation
 
Actually, here h is a Monge representation, h(x,y).

And I just want to solve this equation in 1D.

Could you explain it in details/

Thany you !


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