论文标题
McKendrick-von foerster边界条件的生长碎片方程
Growth-fragmentation equations with McKendrick--von Foerster boundary condition
论文作者
论文摘要
本文涉及生长的良好性和长期渐近性 - 碎片碎片率和麦肯德里克（McKendrick-von foerster）边界条件。我们提供了三种不同的方法，即证明该问题有强烈连续的半群解决方案，并表明它是具有均匀边界条件的相应半群的紧凑扰动。这允许将后期半群的光谱差距上的结果传输到本文中考虑的结果。我们还提供了足够和必要的条件，以证明其具有异步指数增长所需的半群。我们通过为特殊类别的生长问题（McKendrick-von foerster边界条件）提供明确的解决方案，并找到其长期行为的Perron Eigenpair来结束论文。
The paper concerns the well-posedness and long-term asymptotics of growth--fragmentation equation with unbounded fragmentation rates and McKendrick--von Foerster boundary conditions. We provide three different methods of proving that there is a strongly continuous semigroup solution to the problem and show that it is a compact perturbation of the corresponding semigroup with a homogeneous boundary condition. This allows for transferring the results on the spectral gap available for the later semigroup to the one considered in the paper. We also provide sufficient and necessary conditions for the irreducibility of the semigroup needed to prove that it has asynchronous exponential growth. We conclude the paper by deriving an explicit solution to a special class of growth--fragmentation problems with McKendrick--von Foerster boundary conditions and by finding its Perron eigenpair that determines its long-term behaviour.
