Variable in subdomain of another variable's domain

[valentinsulzer]

What is the best way of representing the following system, where u is in x in [0,1] and v is in x in [0,0.5] but depends on the value of u in [0,0.5]?

@parameters t x y
@variables u(..) v(..)
Dt = Differential(t)
Dx = Differential(x)
Dxx = Differential(x)^2
Dyy = Differential(y)^2
eqs  = [Dt(u(t,x)) ~ Dxx(u(t,x)), 
        Dt(v(t,y)) ~ Dyy(v(t,y)) - u(t,y)]
bcs = [u(0,x) ~ - x * (x-1) * sin(x),
       v(0,x) ~ - y * (y-1) * sin(y),
       u(t,0) ~ 0.0, u(t,1) ~ 0.0,
       v(t,0) ~ 0.0, v(t,0.5) ~ 0.0]

domains = [t ∈ IntervalDomain(0.0,1.0),
           x ∈ IntervalDomain(0.0,1.0),
           y ∈ IntervalDomain(0.0,0.5)]

pdesys = PDESystem(eqs,bcs,domains,[t,x,y],[u(t,x),v(t,y)])
discretization = MOLFiniteDifference([x=>0.1,y=>0.1],t)
prob = discretize(pdesys,discretization)
sol = solve(prob,Tsit5())

Maybe both u and v could both be defined on t,x but then the equations for v outside of [0,0.5] could be ignored, based on where the boundary conditions are defined?