what type of equation is this ?


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Topic: Science > Physics
User: "govandi"
Date: 21 Oct 2003 03:39:03 AM
Object: what type of equation is this ?
My apologies if this is a newbie type question.
The Equation of the form Ut + H( Ux, x) = 0
is the Hamilton-Jacobi Equation in 1-D.
What are equations of the following type called?
Ut + H( U, Ux, x) = 0
and what are the numerical techniques used
to solve it ? across a shock ?
.

User: "Igor"

Title: Re: what type of equation is this ? 21 Oct 2003 10:47:04 PM
On 21 Oct 2003 01:39:03 -0700,
(govandi) wrote:

My apologies if this is a newbie type question.

The Equation of the form Ut + H( Ux, x) = 0

is the Hamilton-Jacobi Equation in 1-D.

What are equations of the following type called?

Ut + H( U, Ux, x) = 0

and what are the numerical techniques used
to solve it ? across a shock ?

From what I can gather, U is the classical action given by int (L dt),
sometimes called Hamilton's principle or characteristic function in
this context. You're saying , essentially, that the Hamiltonian is
explicitly dependent on U itself. Just how is H dependent on U?
I.e., what is H (U, Ux, x)?
.


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