Question: solving system of partial differential equations numerically

I am trying to solve the particular system of partial differential equation. But I get the following error.pdsolve.mw
 

"restart;  f(x,y):=x*y:  yy:={diff(f(x,y),x)=0,diff(f(x,y),y)=0}:  ee:=pdsolve(yy,numeric);"

Error, (in pdsolve/numeric) invalid subscript selector

 

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