is there any way of dealing with Delay Partial Differential Equations using DifferentialEquations.jl, MethodsOfLines.jl, or any other package?
Alternatively, has anybody any suggestion/recommendation about how to deal with these problems?
BTW, I take the chance for thanking the Julia community for its fantastic work.
Sure — discretize it in space using whatever method you want, and integrate it in time using the delay differential equations in DifferentialEquations.jl. (This is the “method of lines,” but you don’t necessarily need to use MethodOfLines.jl for your spatial discretization. There are lots of PDE spatial-discretization methods to choose from.)
For now you need to do a manual discretization, though support for DDEs in ModelingToolkit (and thus PDDEs in MethodOfLines later, maybe far later) is something that’s being hacked on in the next few months so it’s in progress but not there yet.