Suppose u=u(x,y) is the solution of the boundary value problem partial^2u/partial x^2+partial^2u/partial y^2+partial u/partial x=0 in (x,y)inmathbb R^2:x^2+y^2<1, u(x,y)=1+2x^2y^2 on (x,y)inmathbb R^2:x^2+y^2=1. Then which of the following statements are true?

Q95Section C (Part C)95 of 120

Maximum principle for $\Delta u+u_x=0$ on the unit disc

Suppose $u=u(x,y)$ is the solution of the boundary value problem

$\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}+\frac{\partial u}{\partial x}=0 \text{ in }\{(x,y)\in\mathbb R^2:x^2+y^2<1\},$

$u(x,y)=1+2x^2y^2 \text{ on }\{(x,y)\in\mathbb R^2:x^2+y^2=1\}.$

Then which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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