论文标题
指数稳定和解决方案对不同规范的初始数据的连续依赖性，用于时空变化的线性抛物线PDE
Exponential stabilization and continuous dependence of solutions on initial data in different norms for space-time-varying linear parabolic PDEs
论文作者
论文摘要
For an arbitrary parameter $p\in [1,+\infty]$, we consider the problem of exponential stabilization in the spatial $L^{p}$-norm, and $W^{1,p}$-norm, respectively, for a class of anti-stable linear parabolic PDEs with space-time-varying coefficients in the absence of a Gevrey-like condition, which is often imposed on PDE的时变系数，用于保证文献中光滑（W.R.T.时间变量）核函数的存在。然后，基于获得的指数稳定性，我们表明，所考虑的系统的解决方案不断取决于$ l^{p} $ - norm-narm和$ w^{1，p} $ - norm-narm-最初数据的差异。为了获得与时间无关的（并因此足够平滑）的函数，而没有类似Gevrey的条件并处理[1,2）$的$ p \时处理的奇点，我们应用了一种组合方法，即，即在lyapunov函数（ALFS）方面的最初依赖（ALFS）的稳定性和近似性的组合，以稳定范围（ALFS），以稳定范围（ALFS），以稳定范围（ALFS），以稳定范围（ALFS），以实现秘密（ALFS），以实现与lyapunov的相差（ALFS）的范围。规范。
For an arbitrary parameter $p\in [1,+\infty]$, we consider the problem of exponential stabilization in the spatial $L^{p}$-norm, and $W^{1,p}$-norm, respectively, for a class of anti-stable linear parabolic PDEs with space-time-varying coefficients in the absence of a Gevrey-like condition, which is often imposed on time-varying coefficients of PDEs and used to guarantee the existence of smooth (w.r.t. the time variable) kernel functions in the literature. Then, based on the obtained exponential stabilities, we show that the solution of the considered system depends continuously on the $L^{p}$-norm, and $W^{1,p}$-norm, respectively, of the initial data. In order to obtain time-independent (and thus sufficiently smooth) kernel functions without a Gevrey-like condition and deal with singularities arising in the case of $p\in[1,2)$, we apply a combinatorial method, i.e., the combination of backstepping and approximation of Lyapunov functionals (ALFs), to stabilize the considered system and establish the continuous dependence of solutions on initial data in different norms.
