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Old   April 7, 2005, 12:01
Default how can solve this equation
  #1
Jianfeng Xia
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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
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Old   April 8, 2005, 13:50
Default Re: how can solve this equation
  #2
Junseok Kim
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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
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Old   April 8, 2005, 13:55
Default Re: how can solve this equation
  #3
Jianfeng Xia
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Thanks a lot, But I have no my own website.

Can I set pdf file to your email box?
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Old   April 8, 2005, 13:59
Default Re: how can solve this equation
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Junseok Kim
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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
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Old   April 8, 2005, 14:02
Default Re: how can solve this equation
  #5
Jianfeng Xia
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OK.

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Old   April 8, 2005, 15:02
Default Re: how can solve this equation
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m. malik
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Will appreciate if you can e-mail me the equation. Thanks
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Old   April 8, 2005, 16:15
Default http://math.uci.edu/~jskim/web.pdf
  #7
Junseok Kim
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Here is the problem description.

http://math.uci.edu/~jskim/web.pdf
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Old   April 9, 2005, 22:28
Default Re: how can solve this equation
  #8
diaw
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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...
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Old   April 10, 2005, 09:31
Default Re: http://math.uci.edu/~jskim/web.pdf
  #9
????
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What is h(X) the profile of? What variable?
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Old   April 10, 2005, 19:26
Default Re: how can solve this equation
  #10
Jianfeng Xia
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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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