Solving a separable PDE with BC

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SUMMARY

The discussion focuses on interpreting boundary conditions (BC) for a separable partial differential equation (PDE), specifically the diffusion equation. The boundary conditions presented are U(0,t) = U(l,t) = 0, which do not equate to a constant value. Participants emphasize the need to clarify how to apply these BCs to the ordinary differential equations (ODEs) derived from the PDE. The discussion encourages sharing the equations obtained by substituting u(x,t) = X(x)T(t) into the boundary conditions for further analysis.

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  • Understanding of partial differential equations (PDEs)
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Mathematicians, physicists, and engineering students dealing with boundary value problems in partial differential equations, particularly those focused on diffusion processes.

trap101
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So I have a question in terms of interpreting the boundary conditions for a PDE. It is question 4 in the attached picture.

My question is that usually when I have encountered BC problems I have been given that my boundary conditions equal a given value, in terms of the diffusion equation:

U(0,t) = U(l,t) = 0,

but as yuo can see they don't equate it to a constant. I know how to solve through for the PDE, but now I'm having trouble interpreting those BC in order to apply them to the ODEs I have obtained. Is there a constant I should assume that they equal?
 

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Show us what equations you get when you let ##u(x,t) = X(x)T(t)## and apply it to the two boundary conditions. And please type it here instead of giving an uneditable image.
 

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