check coercive in Lax-Milgram

Asked Jun 21 '13 at 13:17

Active Jun 21 '13 at 13:17

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Today, I try to solve a PDEs problem, but I have a obstacles:

Let $u\in H^1(0,1)$ such that $u'(1)=-u(1), u'(0)=u(0)$, and $$a(u,u)=u^2(1)+u^2(0)+\int_0^1 (u'(x))^2dx-\int_0^1 (u(x))^2dx$$ define $$||u||_{H^1(0,1)}^2=\int_0^1((u'(x))^2+(u(x))^2)dx$$ Show that $a$ is coercive, i.e. exists $\alpha_0\geq0$ such that $$a(u,u)\geq \alpha_0 ||u||_{H(0,1)}^2$$

asked Jun 21 '13 at 13:17

Muniain

1,543

Can you explain in above specific case? – Muniain Jun 21 '13 at 13:33
I want to confirm that in your definition $$a(u,u)=u^2(1)+u^2(0)+\int_0^1 u'(x)^2dx \color{red}{-}\int_0^1 u(x)^2,dx$$ is it a minus there? – Shuhao Cao Jun 21 '13 at 23:39
Yes. If "+" then so easy to prove – Muniain Jun 22 '13 at 01:30

check coercive in Lax-Milgram

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