∫∂Ω∂u[∂N}dσ if Δu=0 in Ω?Is it always possible to solve an equation u″=0 in [0,1]...

Patricia Crane

Patricia Crane

Answered

2022-01-19

Ωu[N}dσ if Δu=0 in Ω?
Is it always possible to solve an equation u=0 in [0,1] if u(0) and u(1) are given?(What is connection to first question?) Is the solution - unique?

Answer & Explanation

Neil Dismukes

Neil Dismukes

Expert

2022-01-19Added 37 answers

For the first one
From the divergence theorem for the vector field gradu we get that:
Ω÷( u)ν=Ω<u,N>σ
where ν is the volume element.
Using now the ypothesis that 0=Δu=÷( u) and that uN=< g,N>

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?