It is shown that if the dispersion of the KdV equation is replaced by a higher order dispersion ∂xm, where m≥3 is an odd integer, then the critical Sobolev exponent for local well-posedness on the circle does not change. That is, the resulting equation is locally well-posed in Hs(T), s≥−1/2.

The literature on environmental R&D frequently studies innovation as a two-stage process, with a single R&D event leading from a conventional polluting technology to a perfectly clean backstop. We allow for uncertainty in innovation in that the new technology may turn out to generate a new...

The literature on environmental R&D frequently studies innovation as a two-stage process, with a single R&D event leading from a conventional polluting technology to a perfectly clean backstop. We allow for uncertainty in innovation in that the new technology may turn out to generate a new...

Economic growth thus far has been closely linked to the bulk conversion of energy stored in carbon based fuels (wood, coal, oil, natural gas) into useful work. Burning such fuels gives rise to CO2-emissions. These emissions, together with other greenhouse gasses (GHG's) like methane, are now...

This paper solves a second-best problem where a government has in particular to choose whether to tax financial inflows (capital controls) or not, and when. A multi-stage optimal control technique is used to this end. First, it is shown that it is optimal to switch in finite time from capital...

When cheap fossil energy is polluting and pollutant no longer absorbed beyond a certain concentration, there is a moment when the introduction of a cleaner renewable energy, although onerous, is optimal with respect to inter-temporal utility. The cleaner technology is adopted either...