Optimal Control of Global Warming

An optimal control model of global warming is presented and analyzed. The model has two state variables, representing the anthropogenic concentration of greenhouse gases in the atmosphere and the temperature increase due to the greenhouse gas concentration. The state equation for greenhouse gas concentration includes absorption by the environment, but at a rate that is negatively related to temperature increase. Sufficient conditions are offered for a solution with two steady states to exist, and for at least one of the steady states to yield a positive absorption capacity rate. A numerical illustration is offered. Also, a special case of the model is analyzed, in which the environmental absorption capacity rate is assumed fixed