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Pure Mathematics 2024
时间周期双稳型反应扩散方程解的长时间行为
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Abstract:
本文研究以下一类时间周期反应扩散方程ut=uxxuxf(t,u),？x∈R,？t>0.的解的长时间渐近行为，其中，f(t,u)是满足双稳型条件且t具有周期性。将通过引入辅助函数，构造适当的上下解，再运用比较原理，可以得到方程解在无穷远处的性质。
This paper focuses on a class of time-periodic reaction-diffusion equationsut=uxxuxf(t,u),？x∈R,？t>0.of solutions with long time asymptotic behaviour, wheref(t,u)satisfies the bistable condition and t is periodic. The properties of the solutions of the equation at infinity will be obtained by introducing auxiliary functions, constructing appropriate upper and lower solutions, and then applying the comparison principle.
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