tailieunhanh - báo cáo hóa học:" Research Article On the Well Posedness and Refined Estimates for the Global Attractor of the TYC Mod"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On the Well Posedness and Refined Estimates for the Global Attractor of the TYC Mod | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 405816 29 pages doi 2010 405816 Research Article On the Well Posedness and Refined Estimates for the Global Attractor of the TYC Model Rana D. Parshad1 and Juan B. Gutierrez2 1 Department of Mathematics and Computer Science Clarkson University Potsdam NY 13676 USA 2 Mathematical Biosciences Institute Ohio State University Columbus OH 43210 USA Correspondence should be addressed to Rana D. Parshad rparshad@ Received 14 July 2010 Accepted 2 November 2010 Academic Editor Sandro Salsa Copyright 2010 R. D. Parshad and J. B. Gutierrez. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. The Trojan Y Chromosome strategy TYC is a theoretical method for eradication of invasive species. It requires constant introduction of artificial individuals into a target population causing a shift in the sex ratio that ultimately leads to local extinction. In this work we demonstrate the existence of a unique weak solution to the infinite dimensional TYC system. Furthermore we obtain improved estimates on the upper bounds for the Hausdorff and fractal dimensions of the global attractor of the TYC system via the use of weighted Sobolev spaces. These results confirm that the TYC eradication strategy is a sound theoretical method of eradication of invasive species in a spatial setting. It also provides a solid ground for experiments in silico and validates the use of the TYC strategy in vivo. 1. Introduction An exotic species is a species that resides outside its native habitat. When it causes some sort of measurable damage it is often referred to as invasive. The recent globalization process has expedited the pace at which exotic species are introduced into new environments. Once established these species can be extremely difficult to .