  p2pOC is an add-on toolbox to the Matlab package pde2path. It is aimed at the
numerical solution of optimal control (OC) problems with an infinite time
horizon for parabolic systems of PDE over 1D or 2D spatial domains. The basic
idea is to treat the OC problem via the associated canonical system in two
steps. First we use pde2path to find branches of stationary solutions of the
canonical system, also called canonical steady states (CSS). In a second step
we use the results and the spatial discretization of the first step to
calculate the objective values of time-dependent canonical paths ending at a
CSS with the so called saddle point property. This is a (typically very high
dimensional) boundary value problem (BVP) in time, which we solve by combining
a modification of the BVP solver TOM with a continuation algorithm in the
initial states. We explain the design and usage of the package via two example
problems, namely the optimal management of a distributed shallow lake model,
and of a semi-arid grazing system. Both show interesting bifurcations of so
called patterned CSS, and in particular the latter also a variety of patterned
optimal steady states. The package (library and demos) can be downloaded at
www.staff.uni-oldenburg.de/hannes.uecker/pde2path.
