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I am wondering if the boundary conditions for the following linear PDE can be seperated.

$\frac{\partial F(t,x,y)}{\partial t}=\frac{\partial^2 F}{\partial x^2}+\frac{\partial^2 F}{\partial y^2}$

Suppose I have four boundary conditions in a 2D domain that

$F(t,0,y)=1,F(t,1,y)=2,F(t,x,0)=2,\frac{\partial F}{\partial y}|_{y=1}=0$

where $0 \leq x \leq1$ , $0 \leq =y \leq1$

Can I seperate the problem into 4 linear problems with boudanry conditions that

$F(t,0,y)=0,F(t,1,y)=0,F(t,x,0)=0,\frac{\partial F}{\partial y}|_{y=1}=0$

$F(t,0,y)=1,F(t,1,y)=0,F(t,x,0)=0,F(t,x,1)=0$

$F(t,0,y)=0,F(t,1,y)=2,F(t,x,0)=0,F(t,x,1)=0$

$F(t,0,y)=0,F(t,1,y)=0,F(t,x,0)=2,F(t,x,1)=0$

Kai Jiao
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0 Answers0