论文标题
针对边界价值问题的适应性凝血方程
Well-posedness for boundary value problems for coagulation-fragmentation equations
论文作者
论文摘要
我们研究了一个使用边界数据的凝血 - 碎片分散方程，当凝结核的界限为零并显示在应用中相关的奇异内核的溶液时，确定了初始值问题的适当性。我们确定了溶液的巨大时间渐近行为，证明在没有碎片的情况下，解决方案将指数汇合至零，如果边界值满足详细的平衡条件，则解决方案会稳定在平衡的情况下稳定。顺便说一句，我们通过显示积极时间的负矩的有限性来改善解决方案的规律性。
We investigate a coagulation-fragmentation equation with boundary data, establishing the well-posedness of the initial value problem when the coagulation kernels are bounded at zero and showing existence of solutions for the singular kernels relevant in the applications. We determine the large time asymptotic behavior of solutions, proving that solutions converge exponentially fast to zero in the absence of fragmentation and stabilize toward an equilibrium if the boundary value satisfies a detailed balance condition. Incidentally, we obtain an improvement in the regularity of solutions by showing the finiteness of negative moments for positive time.
