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PDE problem

1. We look at a Laplace equation ( [tex]\Delta u(x,y) =o[/tex]) on a square [0, 1]* [0, 1]
If we know that [tex]u_{x=o}[/tex]= siny , [tex]u_{x=1}[/tex]= cosy
[tex]u_y|_{y=0}[/tex]= 0 , [tex]u_y|_{y=1}[/tex]= 0 we differentiate here by y. proove that |u|<=1.






3. The Attempt at a Solution

We now know that the maximum of u has to be on the boundary. If it is greater then one, then it has to be on either y=0 or y =1.
 

Answers and Replies

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Yes, that is true and I would say good enough for an applied math course, with just a little bit more about the maximum value theorem (or whatever it is called) to justify.
 
OK)) Could you tell me what that "little bit " is)?
 
Dick
Science Advisor
Homework Helper
26,258
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The solution to any old PDE doesn't satisfy the maximum principle. The solutions to the Laplace equation do, because they are a special kind of function with a special name. I think mindscrape just wants to you point to the theorem that says that the maximum is on the boundary.
 
Guys, I have solved it!
No more help needed on it!
 

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