[問題]Poisson equation-numerical solutions

[chopriabin ()]

Consider the nonlinear Poisson equation for u=u(x,y) as follows:

u_xx+ u_yy = f(u) in {x,y | x^2+y^2<1}

x*u_x+y*u_y=0     on {x,y | x^2+y^2=1}

Here f(u) is a function which is implicit in u,

and f(u) cannot have an explicit function.

Moreover, by using NDSolve f(u) can be numerically plotted point by point.

Is it possible to use Mathematica to numerically solve

this boundary value problem? Thank you very much!

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推 jumbajuice: 10.0版的新功能: DirichletCondition
→ jumbajuice: http://ppt.cc/Aqyr
→ chopriabin: 這是nonlinear Poisson eqn, 即 laplacian u=f(u)
→ chopriabin: and here f(u) is not equal to 0...
→ chopriabin: 這樣可以用上面你提供的指令做嗎？
→ chopriabin: 最上面加上這句：謝謝你的回應,可問題是Neumann cond.