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