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April 7, 2005, 12:01 
how can solve this equation

#1 
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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 

April 8, 2005, 13:50 
Re: how can solve this equation

#2 
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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 

April 8, 2005, 13:55 
Re: how can solve this equation

#3 
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Thanks a lot, But I have no my own website.
Can I set pdf file to your email box? 

April 8, 2005, 13:59 
Re: how can solve this equation

#4 
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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 

April 8, 2005, 14:02 
Re: how can solve this equation

#5 
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OK.


April 8, 2005, 15:02 
Re: how can solve this equation

#6 
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Will appreciate if you can email me the equation. Thanks


April 8, 2005, 16:15 
http://math.uci.edu/~jskim/web.pdf

#7 
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April 9, 2005, 22:28 
Re: how can solve this equation

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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, 09:31 
Re: http://math.uci.edu/~jskim/web.pdf

#9 
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What is h(X) the profile of? What variable?


April 10, 2005, 19:26 
Re: how can solve this equation

#10 
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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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