- #1
bmxicle
- 55
- 0
Homework Statement
[tex] U_t = u_{xx} - 4U [/tex]
[tex] u_x (0, t) = 0, u_x (\pi, t) = 1 [/tex]
[tex] u(x, 0) = 4cos(4x) [/tex]
Find a steady state solution to the boundary value problem.
Homework Equations
n/a
The Attempt at a Solution
Well I'm quite comfortable solving dirichlet/ mixed boundary value problems of this form. I was under the impression that you must search for a solution of the form
[tex]u(x,t) = w(x,t) + v(x,t)[/tex] where, [tex] w(x, t) = ax^2 + bx + ct[/tex] Since there cannot be a steady state solution because the boundary value rates of change are not equal, so there cannot be a solution that doesn't change with time.
I have the solution, and it sets [tex]U_t = 0[/tex] and goes about finding the 'steady state' solution and finding the eigenfunctions, but that seems wrong to me because of the reasons mentioned above. So I'm just wondering where my thinking is going wrong and why you can find a steady state solution to a neumann boundary value problem of this type.