Here is one of them - i posted it in another thread and i am getting help in there https://www.physicsforums.com/showthread.php?t=91781(adsbygoogle = window.adsbygoogle || []).push({});

this is another of my problems

Show that if C is a piecewise continuously differentiable closed curve bounding D then the problem

[tex] \nabla^2 u= -F(x,y) \ in\ D[/tex]

[tex] u = f \ on \ C_{1} [/tex]

[tex] \frac{\partial u}{\partial n} + \alpha u = 0 \ on \ C_{2} [/tex]

where C1 is a part of C and C2 the remainder and where alpha is a positive constant, has at most one solution.

now i know that [tex] \nabla^2 u = \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = -F(x,y) [/tex]

now im not quite sure how to connect the C1 part to C2 part...

would it be something liek C= C1 + C2?

but how would one go about showing that this has at most ONE solution?? I m not quite sure how to start ... Please help

another one

Show that the problem

[tex] \frac{\partial}{\partial x} (e^x \frac{\partial u}{\partial x} + \frac{\partial}{\partial y} (e^y \frac{\partial u}{\partial y} = 0 \ for \ x^2+y^2 < 1 [/tex]

u = x^2 for x^2 + y^2 = 1

has at most one solution

Hint Use the divergence theorem to derive an energy identity

Perhaps i dont remember a theorem i should have learnt in ap revious class... or i am not familiar with it but what would i use the divergence theorem here?

i eman i can get it down to this

[tex] e^x \frac{\partial}{\partial x} (u + \frac{\partial u}{\partial x}) + e^y \frac{\partial}{\partial y} (u + \frac{\partial u}{\partial y}) = 0 [/tex]

but hereafter i am stuck, please do advise!

Thank you!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Partial DIfferential Equations problems

**Physics Forums | Science Articles, Homework Help, Discussion**