e proceed to verify that the
expression
is a Lagrangian for the heat
equation
We form the "action" function as
follows
and calculate the
variation
hence,
Similarly, the calculation of
leads
to
Unfortunately, general Hamiltonian technique is not applicable to the heat
equation because the defining equation for p
(
generalized impulse equation
)
does not have a solution for q
(
generalized impulse solution
).
