Propagation dynamics of a time periodic diffusion equation with degenerate nonlinearity |
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| Institution: | 1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China;2. Department of Mathematics, University of Central Florida, Orlando, FL 32816, United States;1. Academy of Romanian Scientists, Splaiul Independen?ei 54, 050094 Bucharest, Romania;2. Faculty of Mathematics and Computer Science, Babe?-Bolyai University, 1 M. Kog?lniceanu Str., 400084 Cluj-Napoca, Romania;3. Department of Applied Mathematics, University of Craiova, 13 A.I. Cuza Str., 200585 Craiova, Romania;1. School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, 611756, People’s Republic of China;2. School of Civil Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 611756, People’s Republic of China;1. School of International Programs, Guangdong University of Finance, Guang Zhou, Guangdong Province, 510521, China;2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John''s, Newfoundland, A1 C5S7, Canada |
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| Abstract: | This paper is on study of traveling wave solutions and asymptotic spreading of a class of time periodic diffusion equations with degenerate nonlinearity. The asymptotic behavior of traveling wave solutions is investigated by using auxiliary equations and a limit process. In addition, the monotonicity and uniqueness, up to translation, of traveling wave solution with critical speed are determined by sliding method. Finally, combining super and sub-solutions and the stability of steady states, some sufficient conditions on asymptotic spreading are given, which indicates that the success or failure of asymptotic spreading are dependent on the degeneracy of nonlinearity as well as the size of compact support of initial value. |
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| Keywords: | Traveling wave solution Asymptotic behavior Asymptotic spreading Sliding method |
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