论文标题
关于非自主演化方程的几乎周期性以及对Lotka-Volterra系统的应用
On the almost periodicity of nonautonomous evolution equations and application to Lotka-Volterra systems
论文作者
论文摘要
考虑类型的非自治半线性进化方程：$（\ star）\; u'（t）= a（t）u（t）+f（t，u（t）），\; t \ in \ mathbb {r}，$ where $ a（t），\ t \ in \ mathbb {r} $是Banach Space $ x $中的封闭线性操作员家族，非线性$ f $，在某些真实的interpolation空间上作用于某种真实的interpace（在ups上，都与ups use（即$ tessian）相吻合（即$ tessian $ tessian $ tessian $ tessian $ tessian $ tessian $ tecrand $ tessian $ tecried $ tecried $ tessian。相对于第二个变量的设置。我们使用指数二分法方法证明了方程$（\ star）$的几乎周期性解决方案的存在和独特性。然后，我们通过仅假设第二个变量中的$ f $的连续性来建立Stepanov几乎周期性功能的新组成结果。此外，我们为在广义的几乎周期性环境中的非自主反应扩散方程式的非自治系统提供了一种描述具有扩散和时间依赖性参数的模型。
Consider the nonautonomous semilinear evolution equation of type: $(\star) \; u'(t)=A(t)u(t)+f(t,u(t)), \; t \in \mathbb{R},$ where $ A(t), \ t\in \mathbb{R} $ is a family of closed linear operators in a Banach space $X$, the nonlinear term $f$, acting on some real interpolation spaces, is assumed to be almost periodic just in a weak sense (i.e. in Stepanov sense) with respect to $t$ and Lipschitzian in bounded sets with respect to the second variable. We prove the existence and uniqueness of almost periodic solutions in the strong sense (Bohr sense) for equation $ (\star) $ using the exponential dichotomy approach. Then, we establish a new composition result of Stepanov almost periodic functions by assuming just the continuity of $f$ in the second variable. Moreover, we provide an application to a nonautonomous system of reaction-diffusion equations describing a Lotka-Volterra predator-prey model with diffusion and time-dependent parameters in a generalized almost periodic environment.
