论文标题
在化学恒定中的扩散增长碎片方程的良好姿势和随机推导
Well posedness and stochastic derivation of a diffusion-growth-fragmentation equation in a chemostat
论文作者
论文摘要
我们研究非线性耦合系统的溶液的存在和唯一性，该系统由变性扩散增长碎片方程和差分方程，这是由于化学固醇中细菌生长的建模而产生的。该系统是在大种群近似中得出的，从随机个体的模型中，每个模型都以扩散描述的非负实际有价值特征为特征。突出显示了两个独特结果。它们的假设与资源对单个性状动力学的影响有关的假设有所不同，主要困难是由于这种依赖性和扩散系数的退化而导致的非线性性。此外，我们表明，随机性状动力学的半组通过概率参数允许密度，这使得扩散散布方程的测量解决方案是具有某种规律性的函数。
We study the existence and uniqueness of the solution of a non-linear coupled system constituted of a degenerate diffusion-growth-fragmentation equation and a differential equation, resulting from the modeling of bacterial growth in a chemostat. This system is derived, in a large population approximation, from a stochastic individual-based model where each individual is characterized by a non-negative real valued trait described by a diffusion. Two uniqueness results are highlighted. They differ in their hypotheses related to the influence of the resource on individual trait dynamics, the main difficulty being the non-linearity due to this dependence and the degeneracy of the diffusion coefficient. Further we show that the semi-group of the stochastic trait dynamics admits a density by probabilistic arguments, that allows the measure solution of the diffusiongrowth-fragmentation equation to be a function with a certain Besov regularity.
