# System of two equations

**URL:** <https://community.freefem.org/t/system-of-two-equations/1006>\
**Category:** General Discussion\
**Created:** [June 2, 2021, 8:51pm UTC](https://community.freefem.org/t/system-of-two-equations/1006 "2021-06-02T20:51:21Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Aicha](https://avatars.discourse-cdn.com/v4/letter/a/ec9cab/32.png) [@Aicha](https://community.freefem.org/u/Aicha)\
**Post date:** [June 2, 2021, 8:51pm UTC](https://community.freefem.org/t/system-of-two-equations/1006/1 "2021-06-02T20:51:21Z")

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Hi,  
i have to resolve two following equations in 2D domain : [0,L] x[0,H]  
dV/dt = D\* Delta V - dV/dx - V  
dU/dt= V(x,0,t) - U (where V is the solution of the first equation).  
with boundary conditions  
x=0,L: dV/dx = 0, y=0: dV/dy=- U + V(x,0,t); y=H: dV/dy=0  
avec initial condition V(x,y,0)= V0

My questions are:  
1-how we can exprime V(x,0,t) in the variational formulation of second equation to resolve the system?  
2- How we can define the boundary conditions of V with FF++?

Regards