An optimal control problem for a system of stochastic partial differential equations with nonlocal terms is considered. The control of this system is motivated by a model for optimal harvesting of a population on a spatial grassland habitat. Existence of ...

We consider the optimal control of a two-dimensional steady-state thermistor. The problem is described by a system of two nonlinear elliptic partial differential equations with appropriate boundary conditions which model the coupling of the thermistor ...

We seek to identify the dispersive coefficient in a wave equation with Neumann boundary conditions in a bounded space-time domain from imprecise observations of the solution on the boundary of the spatial domain (Dirichlet data). The problem is ...

We prove existence and uniqueness results for competitive systems consisting of two parabolic equations supplemented with positivity constraints. The coupling terms include local and nonlocal interaction terms. Monotone iteration schemes are used to ...

This paper discusses existence, uniqueness, and a priori estimates for time-dependent and time-independent transport equations with unbounded collision operators. These collision operators are described by second-order differential operators resulting ...

The problem of optimal switching control of a diffusion process with costly switchings leads to a system of fully nonlinear elliptic partial differential equations with implicit obstacles. We obtain results on the existence, uniqueness and regularity of ...