Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Consider $\Delta u =f(x) , x \in \Omega $ and $\nabla u\cdot n +\alpha u = g(x) , x\in \partial\Omega $, where $n$ is outward normal. Can anyone help me to define a bilinear form for this PDE and find out whether its coercive or not ? I am not quite familier how to do it . Thank you So far my progress :

$\int_\Omega \Delta u .v= \int fv $

$-\int_\Omega \nabla u. \nabla v +\int\nabla.( \nabla u v) =\int fv$

using the given relation it can be further written as

$-\int\nabla u .\nabla v -\int \alpha u.v = \int- g\alpha v +\int fv$

ie . Bilinear form is $B[u,v]=\int \nabla u \nabla v +\alpha \int uv $

that means if $\alpha \ge 1 $ then its coercive . Am i right ? Thank you

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.