论文标题
非线性半群以产生家庭及其Lipschitz套装建立
Nonlinear semigroups built on generating families and their Lipschitz sets
论文作者
论文摘要
在一个家庭的适当条件下，$（i（t））_ {t \ ge 0} $ lipschitz在一个完整的度量空间上映射，我们表明，最高到一个副级，强限制$ s（t）：= \ lim_ {n \ to \ to \ to \ infty}（i（t 2^{ - n}）连续半群$（s（t））_ {t \ ge 0} $。当前方法中的共同想法是找到有关发电家族$（i（t））_ {t \ ge 0} $的条件，可以通过迭代将其转移到Semigroup。该结构依赖于Lipschitz套件，在迭代下是不变的，并允许将Lipschitz的连续性保持到极限。此外，我们提供了可验证的条件，该条件可确保Semigroup的无限发电机由$ \ lim_ {h \ downarrow 0} \ tfrac {i（h）x-x} {h} {h} {h} {h} {h} {h} {h} {h} {h} {h} {h} {h} {h h} {h h} n ofer n n n imlim nestim nestimes n ever n unlistime。结果以非线性半群的几个示例（例如鲁棒和线性半群的扰动）进行了说明。
Under suitable conditions on a family $(I(t))_{t\ge 0}$ of Lipschitz mappings on a complete metric space, we show that up to a subsequence the strong limit $S(t):=\lim_{n\to\infty}(I(t 2^{-n}))^{2^n}$ exists for all dyadic time points $t$, and extends to a strongly continuous semigroup $(S(t))_{t\ge 0}$. The common idea in the present approach is to find conditions on the generating family $(I(t))_{t\ge 0}$, which by iteration can be transferred to the semigroup. The construction relies on the Lipschitz set, which is invariant under iterations and allows to preserve Lipschitz continuity to the limit. Moreover, we provide a verifiable condition which ensures that the infinitesimal generator of the semigroup is given by $\lim_{h\downarrow 0}\tfrac{I(h)x-x}{h}$ whenever this limit exists. The results are illustrated with several examples of nonlinear semigroups such as robustifications and perturbations of linear semigroups.
