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Help with PDE problem!


I want to solve the partial differential equations 
with mathematica.
If there is someone who can do this or how to solve
this, then please tell me.
Thank you.

f[x,y,t], g[x,y,t], h[x,y,t] are functions I seek to find
where x, y, t are independent variables.

2 g[x,y,t] - 8 x y D[g[x,y,t],t] - 2 y D[h[x,y,t],t] 
+ 2 y D[g[x,y,t],y] - 2 x D[g[x,y,t],x] - D[h[x,y,t],x]==0,

2 f[x,y,t] - 4 x^2 D[g[x,y,t],t] + 4 y^2 D[g[x,y,t],t] 
- 2 x D[h[x,y,t],t] + 2 x D[g[x,y,t],y] + D[h[x,y,t],y] 
+ 2 y D[g[x,y,t],x]==0,

-2 x D[f[x,y,t],t] + 2 y D[g[x,y,t],t] + D[f[x,y,t],y] 
+ D[g[x,y,t],x]==0,

-2 y D[f[x,y,t],t] - 2 x D[g[x,y,t],t] + D[g[x,y,t],y] 
- D[f[x,y,t],x]==0


Thank you in advance.

I am a graduate student at Seoul National University
                           Department of Mathematics
                           Seoul South Korea  151-742




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