Asymptotic behavior for nonlocal dispersal equations |
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Authors: | Guo-Bao Zhang Wan-Tong Li Yu-Juan Sun |
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Institution: | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China |
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Abstract: | This paper is concerned with the existence and asymptotic behavior of solutions of a nonlocal dispersal equation. By means of super-subsolution method and monotone iteration, we first study the existence and asymptotic behavior of solutions for a general nonlocal dispersal equation. Then, we apply these results to our equation and show that the nonnegative solution is unique, and the behavior of this solution depends on parameter λ in equation. For λ≤λ1(Ω), the solution decays to zero as t→∞; while for λ>λ1(Ω), the solution converges to the unique positive stationary solution as t→∞. In addition, we show that the solution blows up under some conditions. |
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Keywords: | 35K57 35R20 92D25 |
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