Scattering for the Quartic Generalized Benjamin-Bona-Mahony Equation

The generalized Benjamin-Bona-Mahony equation (gBBM) is a model for nonlinear dispersive waves which, in the long-wave limit, is approximately equivalent to the generalized Korteweg-de Vries equation (gKdV). While the long-time behaviour of small solutions to gKdV is well-understood, the corresponding theory for gBBM has progressed little since the 1990s. Using a space-time resonance approach, I establish linear dispersive decay and scattering for small solutions to the quartic-nonlinear gBBM. To my knowledge, this result provides the first global-in-time pointwise estimates on small solutions to gBBM with a nonlinear power less than or equal to five. Owing to nonzero inflection points in the linearized gBBM dispersion relation, there exist isolated space-time resonances without null structure, but in the course of the proof I show these resonances do not obstruct scattering.Comment: 63 pages, 15 figure

The Economic Feasibility of Using Georgia Biomass for Electrical Energy Production

This study investigates the potential for using biomass for the production of electricity in Georgia. The volume, important characteristics, and delivered costs per unit of energy are estimated for various locally produced biomass. Production of synthetic fuels using both pyrolysis and gasification technologies is investigated as potential means for converting biomass into electricity. Capital and operating costs for each of these two technologies are projected across three different scales of production. Estimated costs per unit of electricity generated are determined. It appears, under the conditions modeled, these technologies are not cost competitive with currently used technologies. Significant subsidies would be needed to induce the adoption of these technologies under current economic conditions.bio-electricity, bio-feedstocks, biomass, cost, electricity, Agribusiness, Resource /Energy Economics and Policy,