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Brief introduction
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The goal of this project is the theoretical, numerical analysis and the optimal
control for some nonlinear systems of ode, pde (of parabolic sau elliptic type)
and integro-differential equations which models problems from life and environmental
sciences. We will deal with some models from population dynamics with nonlocal
consumption of resources and the properties of the involved integro-differential
operators. Using the limiting operators we will analyze the fredholm property
of the associated linearized operators, the index, the existence of the traveling
wave solutions and will find solvability conditions and a topological degree. The
discrete case is also of interest. The qualitative analysis (especially the global
stability, the persistence and the bifurcation) of lotka-volterra systems and of
epidemic systems is another goal of our research. Our interes is to construct
state-dependent impulsive control models for predator-prey interactions and to
investigate the existence and orbital stability of nontrivial periodic solutions.
We approach, both theoretically and numerically, some optimal control problems
for models from population dynamics, epidemiology and medicine. Air pollution
models will also be considered.
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