点火型积分-微分方程中的传播速率
Propagation rates in integro-differential equations of ignition type
AI总结：
本文研究点火型积分-微分方程，在含可积卷积核与奇异分数型核的通用框架下，给出精确入侵速率，还获临界情形s=1/2下的首个精确传播估计，区分线性时间与加速 regime。
AI中文摘要：
本文针对非线性点火型积分-微分方程，给出了精确的入侵速率。该框架涵盖可积卷积核与奇异分数型核。尽管从早期研究中可预期跳跃核衰减率1+2s存在阈值，但在这类通用框架中定量结果却少得多。除传播速率外，本研究还提供入侵剖面形状的信息，重要的是，我们得到了临界情形s=1/2下的首个精确传播估计，该情形区分线性时间与加速 regime。
英文摘要：
This paper provides sharp rates of invasion in nonlinear integro-differential equations of ignition type. The framework covers both integrable convolution kernels and singular fractional-type kernels. While the emergence of a threshold on the decay $1+2s$ of the jump kernel is expected from earlier works, far fewer quantitative results were available in such a general framework. In particular, in addition to the spreading rates, our study provides information on the shape of the invasion profiles. Importantly, we obtain the first sharp spreading estimate in the critical case $s=\frac12$, which separates linear-in-time and accelerated regimes.
