Adding a lower and upper bound to PDE values

[LordPontiag]

Dear professor @lululxvi

I want to add lower and upper bounds to the PDEs I'm solving. For example I have a set of Naiver-Stokes Equations as below:

# Transport Equations #################################################
# Continuity equation
f1 = U_x + V_y

# Momentum equations x & y
f2 = (
      U * U_x + V * U_y
      + (1 / rho) * P_x
      - (nu + nu_t) * (U_xx + U_yy)
      )

f3 = (
      U * V_x + V * V_y
      + (1 / rho) * P_y
      - (nu + nu_t) * (V_xx + V_yy)
      )

Then, I want to set a limit range like (0, 10) for the parameter U, (the U_x, U_xx, ... are the derivatives).
I want to add this limit range inside the function of PDEs:

def PDE(X, Y): 
.
.
.
return [f1, f2, f3]

is it possible to do this? or I should use transform function and hard constraints?

[LordPontiag]

Dear professor @lululxvi

I want to add lower and upper bounds to the PDEs I'm solving. For example I have a set of Naiver-Stokes Equations as below:

# Transport Equations #################################################
# Continuity equation
f1 = U_x + V_y

# Momentum equations x & y
f2 = (
      U * U_x + V * U_y
      + (1 / rho) * P_x
      - (nu + nu_t) * (U_xx + U_yy)
      )

f3 = (
      U * V_x + V * V_y
      + (1 / rho) * P_y
      - (nu + nu_t) * (V_xx + V_yy)
      )

Then, I want to set a limit range like (0, 10) for the parameter U, (the U_x, U_xx, ... are the derivatives). I want to add this limit range inside the function of PDEs:

def PDE(X, Y): 
.
.
.
return [f1, f2, f3]

is it possible to do this? or I should use transform function and hard constraints?

I found the answer of this question.
The best way is to apply output transform to answers.