论文标题
部分可观测时空混沌系统的无模型预测
Stability Results for Bounded Stationary Solutions of Reaction-Diffusion-ODE Systems
论文作者
论文摘要
耦合到普通微分方程（ODE）的反应扩散方程可能在空间上表现出低调的固定溶液。这项工作提供了一个全面的理论理论，它是反应扩散 - 电极系统的有限，不连续或连续的固定解的渐近稳定性。我们表征了线性化操作员的光谱，并将其光谱特性与相应的半群特性相关联。 Considering the function spaces $L^\infty(Ω)^{m+k}, L^\infty(Ω)^m \times C(\overlineΩ)^k$ and $C(\overlineΩ)^{m+k}$, we establish a sign condition on the spectral bound of the linearized operator, which implies nonlinear stability or instability of the stationary pattern.
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or continuous, stationary solutions of reaction-diffusion-ODE systems. We characterize the spectrum of the linearized operator and relate its spectral properties to the corresponding semigroup properties. Considering the function spaces $L^\infty(Ω)^{m+k}, L^\infty(Ω)^m \times C(\overlineΩ)^k$ and $C(\overlineΩ)^{m+k}$, we establish a sign condition on the spectral bound of the linearized operator, which implies nonlinear stability or instability of the stationary pattern.
