论文标题
局部质量限制解决方案，用于关键凝血方程
Local mass-conserving solution for a critical Coagulation-Fragmentation equation
论文作者
论文摘要
当初始质量大于$ 1 $时，众所周知，具有乘法凝结和恒定碎片核具有综合凝结和恒定碎片核的临界凝结碎片方程。我们表明，对于任何有限第二刻的给定的阳性初始质量，有一个时间$ t^*> 0 $，因此方程式具有最高$ t^*$的独特质量支持解决方案。新颖的想法是通过小添加术语奇异地扰动恒定的片段化核，并通过伯恩斯坦变换研究扰动系统解决方案的限制行为。
The critical coagulation-fragmentation equation with multiplicative coagulation and constant fragmentation kernels is known to not have global mass-conserving solutions when the initial mass is greater than $1$. We show that for any given positive initial mass with finite second moment, there is a time $T^*>0$ such that the equation possesses a unique mass-conserving solution up to $T^*$. The novel idea is to singularly perturb the constant fragmentation kernel by small additive terms and study the limiting behavior of the solutions of the perturbed system via the Bernstein transform.
