Entire solutions of the Fisher–KPP equation on the half line
| Autor: | Yoshihisa Morita, Bendong Lou, Junfan Lu |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | European Journal of Applied Mathematics. 31:407-422 |
| ISSN: | 1469-4425 0956-7925 |
| DOI: | 10.1017/s0956792519000093 |
| Popis: | In this paper, we study the entire solutions of the Fisher–KPP (Kolmogorov–Petrovsky–Piskunov) equation ut = uxx + f(u) on the half line [0, ∞) with Dirichlet boundary condition at x = 0. (1) For any $c \ge 2\sqrt {f'(0)} $, we show the existence of an entire solution ${{\cal U}^c}(x,t)$ which connects the traveling wave solution φc(x + ct) at t = −∞ and the unique positive stationary solution V(x) at t = +∞; (2) We also construct an entire solution ${{\cal U}}(x,t)$ which connects the solution of ηt = f(η) at t = −∞ and V(x) at t = +∞. |
| Databáze: | OpenAIRE |
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