Electron. J. Differential Equations, Vol. 2020 (2020), No. 59, pp. 1-27.

Nonnegative controllability for a class of nonlinear degenerate parabolic equations with application to climate science

Giuseppe Floridia

We consider a nonlinear degenerate reaction-diffusion equation. First we prove that if the initial state is nonnegative, then the solution remains nonnegative for all time. Then we prove the approximate controllability between nonnegative states via multiplicative controls, this is done using the reaction coefficient as control.

Submitted March 10, 2020. Published June 15, 2020.
Math Subject Classifications: 93C20, 35K10, 35K65, 35K57, 35K58.
Key Words: Semilinear degenerate reaction-diffusion equations; energy balance models in climate science; approximate controllability; multiplicative controls; nonnegative states.

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Giuseppe Floridia
Università Mediterranea di Reggio Calabria
Dipartimento Patrimonio, Architettura, Urbanistica
Via dell'Università 25, Reggio Calabria, 89124, Italy
email: floridia.giuseppe@icloud.com

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