The discussion centers on the uniqueness of solutions to the Poisson equation under mixed boundary conditions, specifically when combining Dirichlet and Neumann boundary conditions. Participants explore the implications of having different types of boundary conditions and question how a unique solution can exist in such scenarios.
Participants express disagreement regarding the uniqueness of solutions under mixed boundary conditions, with no consensus reached on the matter.
The discussion lacks specific examples or mathematical proofs to support the claims made, and the assumptions underlying the boundary conditions are not fully explored.
It has a unique solution for each specified set of boundary conditions.ajeet mishra said:My professor told that poission equation has a unique solution even for mixed boundary conditions( i.e. Dirichlet bc for some part and Neumann for the remaining part). But how is this possible? As different boundary conditions for the same problem will give different solutions.
But how? As there are unique solutions for drichlet and neumann conditions separately and these, in general, may not be consistent.Chestermiller said:It has a unique solution for each specified set of boundary conditions.
Can you provide a specific example (or examples) to illustrate what you are saying?ajeet mishra said:But how? As there are unique solutions for drichlet and neumann conditions separately and these, in general, may not be consistent.