In this paper we prove the existence of global classical solutions to continuous coagulation–fragmentation equations with unbounded coefficients under the sole assumption that the coagulation rate is dominated by a power of the fragmentation rate, thus improving upon a number of recent results by not requiring any polynomial growth bound for either rate. This is achieved by proving a new result on the analyticity of the fragmentation semigroup and then using its regularizing properties to prove the local and then, under a stronger assumption, the global classical solvability of the coagulation–fragmentation equation considered as a semilinear perturbation of the linear fragmentation equation. Furthermore, we show that weak solutions of the coagulation–fragmentation equation, obtained by the weak compactness method, coincide with the classical local in time solutions provided the latter exist.

中文翻译：

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具有无界系数的连续凝结-破碎方程的整体解

在本文中，我们证明了具有无限约束系数的连续凝结-破碎方程的全局经典解的存在，其唯一假设是凝结速率由破碎率的幂决定，因此不需要任何其他改进就可以改进最近的结果多项式的增长受任一比率的限制。这是通过证明碎片半群的分析性的新结果，然后使用其正则化性质证明局部，然后在一个更强的假设下，将凝结-碎片方程的整体经典可解性视为对链的半线性扰动来实现的。线性碎片方程。此外，我们显示了通过弱密实度方法获得的凝结-破碎方程的弱解，