论文标题
关于抽象耦合双曲线 - 促羟基蛋白酶系统的稳定性注释：奇异案例
Note on stability of an abstract coupled hyperbolic-parabolic system: singular case
论文作者
论文摘要
在本文中，我们试图完成耦合的超质和抛物线方程的抽象系统的稳定性分析， = u_1，w（0）= w_0，\ end {array} \ right。 $$ $ a $是复杂的Hilbert Space $ h $上的自动化，正定运算符，而[0,1] \ times [0,1] $ in \ cite {amk}中的$（α，β）\ in [0,1] \ times [0,1] $，以及之后，在\ cite {cite {liu1}中。我们的贡献是确定溶液在区域$ s_3：= \ left \ {（α，β）\ in [0,1] \ times [0,1]中的良好规模; \，β<2α-1\ right \} $考虑了零以奇异性的存在。
In this paper we try to complete the stability analysis for an abstract system of coupled hyperbolic and parabolic equations $$ \left\{ \begin{array}{lll} \ds u_{tt} + Au - A^αw = 0, \\ w_t + A^αu_t + A^βw = 0,\\ u(0) = u_0, u_t(0) = u_1, w(0) = w_0, \end{array} \right. $$ where $A$ is a self-adjoint, positive definite operator on a complex Hilbert space $H$, and $(α, β) \in [0,1] \times [0,1]$, which is considered in \cite{Amk}, and after, in \cite{liu1}. Our contribution is to identify a fine scale of polynomial stability of the solution in the region $ S_3: = \left\{(α,β) \in [0,1] \times [0,1]; \, β< 2α-1 \right\}$ taking into account the presence of a singularity at zero.
