start PDESystem documentation

Author: ChrisRackauckas

docs/src/systems/PDESystem.md

@@ -1,3 +1,26 @@
 # PDESystem
 
-`PDESystem` is still a work in progress.
+#### Note: PDESystem is still experimental and the solver ecosystem is being developed
+
+`PDESystem` is the common symbolic PDE specification for the Julia ecosystem.
+It is currently being built as a component of the ModelingToolkit ecosystem,
+but it will soon be siphoned off to a PDE.jl which defines and documents the
+whole common PDE interface ecosystem. For now, this portion documents the `PDESystem`
+which is the core symbolic component of this interface.
+
+## Vision
+
+The vision for the common PDE interface is that a user should only have to specify
+their PDE once, mathematically, and have instant access to everything as simple
+as a finite difference method with constant grid spacing, to something as complex
+as a distributed multi-GPU discrete Galerkin method.
+
+The key to the common PDE interface is a separation of the symbolic handling from
+the numerical world. All of the discretizers should not "solve" the PDE, but
+instead be a conversion of the mathematical specification to a numerical problem.
+These elementary problems, such as solving linear systems `Ax=b`, solving nonlinear
+systems `f(x)=0`, ODEs, etc. are all defined by DiffEqBase.jl, which then numerical
+solvers can all target these common forms. Thus someone who works on linear solvers
+doesn't necessarily need to be working on a DG or finite element library, but
+instead "linear solvers that are good for matrices A with properties ..." which
+are then accessible by every other discretization method in the common PDE interface.