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

Abstract

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.

Keywords

• semilinear degenerate reaction-diffusion equations
• energy balance models in climate science
• approximate controllability
• multiplicative controls
• nonnegative states