Set differential equations are usually formulated in terms of the Hukuhara differential. As a consequence, the theory of set differential equations is perceived as an independent subject, in which all results are proved within the framework of the Hukuhara calculus. We propose to reformulate set differential equations as ordinary differential equations in a Banach space by identifying the convex and compact subsets of ℝd with their support functions. Using this representation, standard existence and uniqueness theorems for ordinary differential equations can be applied to set differential equations. We provide a geometric interpretation of the main result, and demonstrate that our approach overcomes the heavy restrictions that the use of the Hukuhara differential implies for the nature of a solution.

Herbicides are the foundation of weed control in commercial crop-production systems. However, herbicide-resistant (HR) weed populations are evolving rapidly as a natural response to selection pressure imposed by modern agricultural management activities. Mitigating the evolution of herbicide resistance depends on reducing selection through diversification of weed control techniques, minimizing the spread of resistance genes and genotypes via pollen or propagule dispersal, and eliminating additions of weed seed to the soil seedbank. Effective deployment of such a multifaceted approach will require shifting from the current concept of basing weed management on single-year economic thresholds.