- #1
Scootertaj
- 97
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1. Problem Statement
Solve by inspection the Dirichlet problem, where [itex]\Omega[/itex] is the unit square 0[itex]\leq[/itex]x[itex]\leq[/itex]1, 0[itex]\leq[/itex] y [itex]\leq[/itex] 1, and where the data is:
f(x,y) = {
x for 0[itex]\leq[/itex]x[itex]\leq[/itex]1, y=0,
1 for x = 1, 0[itex]\leq[/itex] y [itex]\leq[/itex] 1,
x for 0[itex]\leq[/itex]x[itex]\leq[/itex]1, y=1,
0 for x=0, 0[itex]\leq[/itex]y[itex]\leq[/itex]1
Dirichlet Problem:
[itex]\Delta[/itex] u = 0 in [itex]\Omega[/itex]
u = f on d[itex]\Omega[/itex]
I don't know where to really start with this one. What does it mean "solve by inspection the dirichlet problem?" What is u? How does the "data" help, it's the initial conditions right?
Solve by inspection the Dirichlet problem, where [itex]\Omega[/itex] is the unit square 0[itex]\leq[/itex]x[itex]\leq[/itex]1, 0[itex]\leq[/itex] y [itex]\leq[/itex] 1, and where the data is:
f(x,y) = {
x for 0[itex]\leq[/itex]x[itex]\leq[/itex]1, y=0,
1 for x = 1, 0[itex]\leq[/itex] y [itex]\leq[/itex] 1,
x for 0[itex]\leq[/itex]x[itex]\leq[/itex]1, y=1,
0 for x=0, 0[itex]\leq[/itex]y[itex]\leq[/itex]1
Homework Equations
Dirichlet Problem:
[itex]\Delta[/itex] u = 0 in [itex]\Omega[/itex]
u = f on d[itex]\Omega[/itex]
The Attempt at a Solution
I don't know where to really start with this one. What does it mean "solve by inspection the dirichlet problem?" What is u? How does the "data" help, it's the initial conditions right?