标题： 关于时间加权空间中拟线性演化方程的线性化稳定性原理 显示英文标题

标题： On the principle of linearized stability for quasilinear evolution equations in time-weighted spaces

摘要： 拟线性（和半线性）抛物型问题形式为$v'=A(v)v+f(v)$，在函数$v\mapsto f(v)$和拟线性部分$v\mapsto A(v)$的定义域之间存在严格包含关系$\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$，是在时间加权函数空间的框架下考虑的。 这使得能够在介于$\mathrm{dom}(f)$和$\mathrm{dom}(A)$之间的中间空间中建立线性化稳定性原理，并在演化过程中相对于相空间具有更大的灵活性。 在微分方程的应用中，这些中间空间可能对应于表现出尺度不变性的临界空间。 提供了几个例子来展示结果的适用性。 显示英文摘要

摘要： Quasilinear (and semilinear) parabolic problems of the form $v'=A(v)v+f(v)$ with strict inclusion $\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the function $v\mapsto f(v)$ and the quasilinear part $v\mapsto A(v)$ are considered in the framework of time-weighted function spaces. This allows one to establish the principle of linearized stability in intermediate spaces lying between $\mathrm{dom}(f)$ and $\mathrm{dom}(A)$ and yields a greater flexibility with respect to the phase space for the evolution. In applications to differential equations such intermediate spaces may correspond to critical spaces exhibiting a scaling invariance. Several examples are provided to demonstrate the applicability of the results.