多维非局部Fisher-KPP方程的大时间行为
Large time behaviour in the multidimensional nonlocal Fisher-KPP equation
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- School of Mathematical Sciences, University of Science and Technology of China（中国科学技术大学数学科学学院）
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中文总结 AI 辅助
本文研究多维非局部Fisher-KPP方程等值集的扩张，推导出渐近对数延迟及方向依赖的常数修正项，深化了Freidlin-Gärtner型公式的精度。
中文摘要 AI 辅助
本文研究了Fisher-KPP型反应-扩散方程解的等值集的扩张，其中扩散由一个非负、紧支撑、偶的核给出。由于该核未被假设为球对称的，等值集以由Freidlin-Gärtner型公式给出的渐近速度前进。本文的主要贡献是将扩张推进到随时间趋于无穷而消失的项，包括一个渐近对数延迟，并由一个在时间上恒定但依赖于传播方向的函数进行修正。
英文摘要
This work studies the expansion of the level sets of the solutions of a Fisher-KPP type reaction- diffusion equation, the diffusion being given by a nonnegative, compactly supported, even kernel. Because the latter is not assumed to be spherically symmetric, the level sets advance at an asymptotic speed given by a Freidlin-Gärtner type formula. The main contribution of this paper is to push the expansion up to terms that vanish as time goes to infinity, consisting in an asymptotically logarithmic delay corrected by an function that is constant in time, but depends on the direction of propagation.
