Maximum order of essential and natural conditions

[ENgez]

Main Question or Discussion Point

Is there a physical explanation for why when given a differential equation with spatial derivative of spatial order $2m$ the maximum order of the essential (displacement) boundary condition is $m$, and the maximum order of the natural (force) boundary condition is $2m-1$

for example, the equaiton governing the dynamic behavior of a 1D bar is:
$\frac{\partial ^{2}u}{\partial x^2} = \frac{1}{c^2} \frac{\partial ^{2}u}{\partial t^2}$

the maximum order of the essential boundary condition is 0 :
$u(0,t)=0$
and the maximal order of the natural boundary condition is 1:
$EA\frac{\partial u}{\partial x}(L,t)=R(t)$

 

[Greg Bernhardt]

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?