无界区域上神经元场的渐近行为
Asymptotic Behavior of neural fields in an unbounded domain
摘要：
本文证明了由方程$$ \frac{\partial u}{\partial t}(x,t)+u(x,t)= \int_{\mathbb{R}^{N}}J(x-y)(f( u(y,t))dy+ h, \quad h > 0, \quad x\in \mathbb{R}^{N}, \quad t\in\mathbb{R}_{+} $$生成的流在权空间$L^{p}(\mathbb{R}^{N}, ρ)$中的紧全局吸引子的存在性。我们也给出了吸引子大小的一致估计，并给出了由该方程产生的流的一个李雅普诺夫泛函
英文摘要：
In this paper, we prove the existence of a compact global attractor for the flow generated by equation $$ \frac{\partial u}{\partial t}(x,t)+u(x,t)= \int_{\mathbb{R}^{N}}J(x-y)(f( u(y,t))dy+ h, \quad h > 0, \quad x\in \mathbb{R}^{N}, \quad t\in\mathbb{R}_{+} $$ in the weight space $L^{p}(\mathbb{R}^{N}, ρ)$. We also give uniform estimates on the size of the attractor and we exhibit a Lyapunov functional to the flow generated by this equation
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
