Question: Equating partial derivative to zero

In PDEtools, suppose to I wish assign zero value to certain first order partial derivative such that higher order derivatives automatically vanish in subsequent excutions, how I can do that?

 

with(PDEtools):

alias(u = u(x, y, t))

u

(1)

Suppose we wish following derivative equal to zero,

diff(u, x) = 0

diff(u, x) = 0

(2)

If we use ":=" for value assignment we will get error. Under above assuption how can we make following derivatives zero?

diff(u, x, x); 1; diff(u, x, y); 1; diff(u, x, x, x, y)

diff(diff(u, x), x)

 

diff(diff(u, x), y)

 

diff(diff(diff(diff(u, x), x), x), y)

(3)

``

 

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