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...

By deriving the necessary conditions for a multi-stage discounted optimal control problem where the endogenous switching instants between regimes appear as an argument of the objective function and the state equation, we analyze the optimal pattern of technology adoption under embodiment with a...

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...

We consider an optimal technology adoption AK model in line with Boucekkine Krawczyk and Vallée (2011): an economy, caring about consumption and pollution as well, starts with a given technological regime and may decide to switch at any moment to a cleaner technology at a given permanent or...

We consider a general control problem with two types of optimal regime switch. The first one concerns technological and/or institutional regimes indexed by a finite number of discrete parameter values, and the second features ecological-like regimes relying on given threshold values for given...

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...

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...