3-rd order partial differential equation

Dear Tomek:

With a lot more information, you could "simply" do a numerical solution.

David A. Smith

You could simplify using Laplace transforms.

(x,t)-(position,

No, I'm an mathematician whos investigating the properties of such an equations, and I'm looking for a physical example.

Dear Tomek:

Third order differential equations come up in motion control. Called "jerk". Higher (than 3) order differentials also have names. Robotics will involve x, y, z, and spin axes, all wrt time. You won't find these commonly modelled outside of motion control, in much more than second order. Navier Stokes is second order, and is used in modelling fluid flow. Second order equations come up in vibration analysis, with potentially thousands of interrelated "dimensions".

Might be some chemical examples, but none comes to mind right away...

General Relativity is currently second order pde. I'm not sure where physics is in this "scale of complexity", though you might ask on sci.physics (if you can tolerate the noise).

David A. Smith

U¿ytkownik "N:dlzc D:aol T:com (dlzc)" napisa³ w wiadomo¶ci news:a8wNd.25195$Yu.24198@fed1read01... physical example.

But partial d.eq. ?....

Dear Tomek:

Im looking for an physical plant ( mechanical, electrical, heat spreding etc. ) whose mathematical model is: partial differential equation of two independent variables (x,t)- (position, time), THIRD order differential respect to time, and

2 and/or 4 order derivatuves respect to x.

Are you asking if anyone has ever seen exactly the formula you didn't actually specify?

Something like: partial-d^3(f)/partial-d(t)^3 + partial-d^2(f)/partial-d(x)^2 = g ... perhaps?

Only second order in this finance (!!!) paper: URL:

third order wave amplitude in a surface wave (Korteweg-deVries equation)

Using google advanced with the exact phrase: third order partial differential equation I get 133 hits, which should be manageable

Using google advanced with the exact phrase: fourth order partial differential equation I get 280 hits, which should also be manageable

Using google advanced with the exact phrase: nth order partial differential equation I get 2 hits.

Does it come up ever? Yes. Does it come up often? No. Do most math packages handle them? Yes. (With lots of caveats.)

David A. Smith

U¿ytkownik "N:dlzc D:aol T:com (dlzc)" napisa³ w wiadomo¶ci news:I5zNd.25225$Yu.20172@fed1read01...

The KdV Equation is nearly ideal ( after changing the variables xt, what is feasible for me ) with its third derivater. Unfortunately the remaining variable (t) is in odd order ( first ) :((((, wchich yields no-sefladjoint differential operator. Im looking for an example of my mathematical research of 3rd order abstract diff.eq., but the remaining variable must yield selfadjoint differential operators ( with pure real discrete eigenvalues ).

I'll try it....

In a heating example, a PDE with a 3rd order with respect to time component would be equivalent to some sort of variable heating condition, like heat generation or convection, right? Maybe something like a rod or plate spinning in a bright light, and/or oscillating closer to the source?

As far as 4th order with respect to x, that's pretty wierd, and I never had anything like that in my PDE class. You'd probably be able to get a 4th order component wrt x if you assigned some crazy material properties that varied as a function of x, like density and/or conductivity.

Hope that helps, Dave

Classical plate theory is 4th order.