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| In this talk, we show the global approximate multiplicative controllability for a class of nonlinear degenerate 1-D reaction-diffusion equations.
First, we obtain embedding results for weighted Sobolev spaces, that proved decisive in reaching well-posedness for nonlinear degenerate problems. Then, we show that the above systems can be steered in $L^2$ from any nonzero, nonnegative initial state into any neighborhood of any desirable nonnegative target-state by bilinear piecewise static controls. Moreover, we extend the above result relaxing the sign constraint on the initial date.
We note that, for a special choise of the diffusion coefficient, the linear part of the above equations reduces to the one of the Budyko-Sellers climate model. This model is an energy balance model which attempts to study the evolution of the temperature on the Planet Earth, as a result of the interaction between large ice masses and solar radiation, see, for instance, [J.I.Diaz, G.Hetzer, L.Tello, An Energy Balance Climate Model with Hysteresis, Nonlinear Analysis
64 (2006), 2053--2074]. |
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