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Sharp estimates for the spreading speeds of the Lotka-Volterra diffusion system with strong competition

Authors:	Rui Peng Chang-Hong Wu Maolin Zhou

Institution:	1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu Province, People''s Republic of China;2. Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan, Republic of China;3. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, People''s Republic of China;1. IMPA, Estrada Dona Castorina 110, Rio de Janeiro 22460-320, RJ, Brazil;2. IMECC-UNICAMP, Rua Sérgio Buarque de Holanda, 651, 13083-859, Campinas-SP, Brazil;3. Center for Mathematical Analysis, Geometry and Dynamical Systems, Department of Mathematics, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;1. Department of Mathematics, Temple University, Philadelphia, PA 19122, United States of America;2. Instituto Argentino de Matemática A. P. Calderón, CONICET, Buenos Aires, Argentina

Abstract:	This paper is concerned with the classical two-species Lotka-Volterra diffusion system with strong competition. The sharp dynamical behavior of the solution is established in two different situations: either one species is an invasive one and the other is a native one or both are invasive species. Our results seem to be the first that provide a precise spreading speed and profile for such a strong competition system. Among other things, our analysis relies on the construction of new types of supersolution and subsolution, which are optimal in certain sense.

Keywords:	Lotka-Volterra diffusion system Strong competition Traveling waves Long-time behavior Spreading speed and profile
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