tastydragoon332
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- May 2, 2024
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Difficult PDE related problem
- Thread starter tastydragoon332
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You didn't say anything about [imath]K[/imath] and [imath]\alpha[/imath]. Are they constants or functions?
We cannot solve this PDE directly because one of the boundary conditions is nonhomogeneous. Therefore, we will have to split the solution [imath]u(x,t)[/imath] into two parts [imath]v(x)[/imath] and [imath]w(x,t)[/imath].
[imath]u(x,t) = v(x) + w(x,t)[/imath]
The first part [imath]v(x)[/imath] will take care of the nonhomogeneous boundary condition while [imath]w(x,t)[/imath] will have homogeneous boundary conditions.
If you are serious to solve this PDE, substitute the new guessed solution [imath]u(x,t) = v(x) + w(x,t)[/imath] into the PDE, and let us see what you get.
This is one way to solve the problem. Another way to solve the problem is to think what happens in the steady state?
Hint: [imath]u_t = 0[/imath]
You have to post this second PDE problem in a new thread if you want us to discuss its solution.
We cannot solve this PDE directly because one of the boundary conditions is nonhomogeneous. Therefore, we will have to split the solution [imath]u(x,t)[/imath] into two parts [imath]v(x)[/imath] and [imath]w(x,t)[/imath].
[imath]u(x,t) = v(x) + w(x,t)[/imath]
The first part [imath]v(x)[/imath] will take care of the nonhomogeneous boundary condition while [imath]w(x,t)[/imath] will have homogeneous boundary conditions.
If you are serious to solve this PDE, substitute the new guessed solution [imath]u(x,t) = v(x) + w(x,t)[/imath] into the PDE, and let us see what you get.
This is one way to solve the problem. Another way to solve the problem is to think what happens in the steady state?
Hint: [imath]u_t = 0[/imath]
You have to post this second PDE problem in a new thread if you want us to discuss its solution.
The solution to this problem is very long. Giving the OP little hints will not bite the posting guidelines. The probability the OP is going to respond to this post is very low. Even when this low happens, the OP is not going anywhere with this PDE without his contribution.
Thank you a lot professor Steven for emphasizing on this matter.
