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

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

Thanks a lot, But I have no my own website.

Can I set pdf file to your email box?

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

OK.

Will appreciate if you can e-mail me the equation. Thanks

Here is the problem description.

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

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...

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

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 !