  We formulate nonlinear nonlocal integro-PDE with memory, biloaded (boundary
integrals load the ambient space, and the ambient space loads the boundary),
and the associated optimal control problems. We derive part of the necessary
conditions for optimality in the form of Hamilton-Euler-Lagrange loaded
integro-PDEs. In the process, we introduce an agglomeration of new differential
operators. Our results have relevance to optimal amelioration of flooded areas,
remediation of sites of contaminated groundwater, and active control methods
for optimally extinguishing forest fires.
