CAS PROJECT. Isotherms. Find the steady-state solutions (temperatures) in the sq

Question

CAS PROJECT. Isotherms.
Find the steady-state solutions (temperatures) in the square platein Fig. 297 with a = 2 satisfying the following boundaryconditions. Graph isotherms.
a) u = sin ?x on the upper side, 0 on the others.
b) u = 0 on the vertical sides, assuming that the other sides areperfectly insulated.
c) Boundary conditions of your choice (such that the solution isnot identically zero).

CAS PROJECT. Isotherms. Find the steady-state solutions (temperatures) in the square platein Fig. 297 with a = 2 satisfying the following boundaryconditions. Graph isotherms. a) u = sin ?x on the upper side, 0 on the others. b) u = 0 on the vertical sides, assuming that the other sides areperfectly insulated. c) Boundary conditions of your choice (such that the solution isnot identically zero).

Explanation / Answer

Dirichlet Problem in a Rectangle R (Fig. 296). We consider a Dirichlet problem for Laplace

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