论文标题
Cauchy的问题是圆环上一类线性退化进化方程
The Cauchy problem for a class of linear degenerate evolution equation on the torus
论文作者
论文摘要
我们在周期性的环境中研究了与操作员$ p（t，d_ {x}，d_ {t}）= d_ {t} - a_ {2}（t）Δ__{x} + sum______________ = 1}} a__} a____________ { a_ {0}（t）$，带有$ t> 0 $，$ t \ in [0，t] $和$ a_ {2}，a_ {1,1}，\ ldots，a_ {1，n}，a_ {0} \ in c \ in c \ inc \ weft（[0，t]; \ nathbbbbbbbb {c} c} $。使用傅立叶分析技术，我们获得了Sobolev，平滑，gevrey和真实分析框架中一类退化初始值问题的完整表征。
We study, in the periodic setting, the well-posedness of the Cauchy problem associated to the operator $P(t, D_{x}, D_{t}) = D_{t} - a_{2}(t) Δ_{x} + \sum_{j = 1}^{N} a_{1, j}(t) D_{x_{j}} + a_{0}(t)$, with $T> 0$, $t \in [0, T]$ and $a_{2}, a_{1,1}, \ldots, a_{1, N}, a_{0} \in C \left([0, T]; \mathbb{C} \right)$. Using Fourier analysis techniques, we obtain a complete characterization for the well-posedness of a class of degenerate initial-value problems in the Sobolev, Smooth, Gevrey and Real-analytic frameworks.
