Abstract In this paper, we study inverse boundary problems associated with semilinear parabolic systems in several scenarios where both the nonlinearities and initial data can be unknown. We establish simultaneous recovery results showing that passive or active Dirichlet-to-Neumann operators uniquely recover of unknowns, even stably a certain case. It turns out play critical role deriving these...

1. Global Energy Problems and the Role of Renewables 1.1. Energy demand 1.2. Energy, environmental problems and sustainable development 1.3. Water demand and consumption 1.4. Water and energy 1.5. Desalination and energy 1.6. Renewable energy technologies 2. Solar Collectors 2.1. Parabolic trough collectors 2.2. Fresnel collectors 2.3. Parabolic dish reflector 2.4. Heliostat field collector 3. ...

in this paper, the optimal boundary control problem for distributed parabolic systems, involving second orderoperator with an infinite number of variables, in which constant lags appear in the integral form both in the state equations and in the boundary condition is considered. some specific properties of the optimal control arediscussed.

We consider fully nonlinear weakly coupled systems of parabolic equations on a bounded reflectionally symmetric domain. Assuming the system is cooperative we prove the asymptotic symmetry of positive bounded solutions. To facilitate an application of the method of moving hyperplanes, we derive Harnack type estimates for linear cooperative parabolic systems.