We consider an optimal control problem which serves as a mathematical model for several problems in economics and management.The problem is the minimization of a continuous constrained functional governed by a linear parabolic diffusion-advection equation controlled in a coefficient in advection part.The additional constraint is non-negativity of a solution of state equation.We construct and analyze several mesh schemes approximating the formulated problem using finite difference methods in space and in time.All these approximations keep the positivity of the solutions to mesh state problem,either unconditionally or under some additional constraints to mesh steps.This allows us to remove corresponding constraint from the formulation of the discrete problem to simplify its implementation.Based on theoretical estimates and numerical results,we draw conclusions about the quality of the proposed mesh schemes.
Taking into account the fact of global economic integration,this paper improves the RICE model and the MRICES model,and establishes a new integrated assessment model MRICES-2012,which takes Ramsey utility as the standard of fairness.Based on the model,schemes which meet the global emission mitigation targets as well as the interests of developing countries are simulated to assess the international fairness of emission reduction.Therefore,a new feasible scheme is proposed,which can not only reach the Copenhagen Consensus but also ensure interests of every country.Specifically speaking,the US and Japan cut emissions 80% and 70% respectively by 2050 relative to the 1990 level;the EU and other developed countries cut 80% by 2050 relative to 1990 level;high human development countries cut 50% by 2050 relative to 1990 level;all above-mentioned countries start emission reduction from 2020 and keep emission on 2050 level by 2100;China begins emission reduction from 2030 and cuts emission 15% by 2050 and 25% by 2100 relative to 2005 level;medium human development countries keep emission on 2020 level by 2100;low human development countries do not take part in reduction on emission intensity and global emission.
Reducing Emissions from Deforestation and Forest Degradation(REDD+) and enhancing "removals of greenhouse gas emissions by forests" in developing countries through positive incentives is regarded as an essential component of the post-2012 climate regime for stabilizing greenhouse gas emissions and an important way of engaging developing countries in global mitigation efforts. We aimed to evaluate the potential effectiveness of REDD+ by integrating it into a land use option framework. One of our goals was to develop scenarios for evaluating the impacts of land use changes on carbon and environmental processes. In addition, we aimed to quantify the potential economic benefits to society of compensated reductions and to identify hotspots for applying REDD+. Three land use change scenarios were examined:(I) business as usual(BAU),(II) economic development, and(III) REDD+. A case study in Indonesia was examined using these land use scenarios and policy interventions, evaluating their effects on carbon emissions, socioeconomics, and environmental features of a spatial system using land use models. Significant emissions and water erosion reductions were predicted to be achieved under the REDD+ scenario, due to reduced deforestation of <6% over the next decade; >0.14 Mt CO2 e reduction was predicted relative to the BAU scenario. Furthermore, the spatial land use model indicated that REDD+ payments of forest carbon credits in the compliance market would play a key role in compensating rural communities and plantation companies for their opportunity cost in ending deforestation. This study provides an example of integrating land use modeling with a scenario analysis framework to evaluate plausible future forecasts and to evaluate the potential impacts of REDD+.
