Initial and Boundary condition example

using EarthSciMLBase
using ModelingToolkit, DomainSets

# Set up ODE system
@parameters x y t
@variables u(t) v(t)
Dt = Differential(t)

x_min = y_min = t_min = 0.0
x_max = y_max = 1.0
t_max = 11.5

eqs = [
    Dt(u) ~ √abs(v),
    Dt(v) ~ √abs(u),
]

@named sys = ODESystem(eqs)

# Create constant initial conditions = 16.0 and boundary conditions = 4.0.
icbc = DomainInfo(
    constIC(4.0, t ∈ Interval(t_min, t_max)),
    constBC(16.0,
        x ∈ Interval(x_min, x_max),
        y ∈ Interval(y_min, y_max),
    ),
)

# Convert to PDESystem and add constant initial and boundary conditions.
pdesys = sys + icbc

pdesys.bcs

\[ \begin{align} u\left( 0, x, y \right) =& 4 \\ v\left( 0, x, y \right) =& 4 \\ u\left( t, 0, y \right) =& 16 \\ u\left( t, 1, y \right) =& 16 \\ u\left( t, x, 0 \right) =& 16 \\ u\left( t, x, 1 \right) =& 16 \\ v\left( t, 0, y \right) =& 16 \\ v\left( t, 1, y \right) =& 16 \\ v\left( t, x, 0 \right) =& 16 \\ v\left( t, x, 1 \right) =& 16 \end{align} \]