一维反应扩散平流系统的惯性流形。第一部分：Dirichlet和Neumann边界条件
Inertial manifolds for 1D reaction-diffusion-advection systems. Part I: Dirichlet and Neumann boundary conditions
摘要：
这是我们研究一维反应-扩散-平流方程组惯性流形的第一部分，主要讨论Dirichlet或Neumann边界条件。虽然这个问题最初并不具有谱隙性质，它表明，这一性质是满足适当的非局部变化后的因变量。在我们研究的第二部分中考虑了周期边界条件的情况，其中情况主要不同，惯性流形可能不存在。
英文摘要：
This is the first part of our study of inertial manifolds for the system of 1D reaction-diffusion-advection equations which is devoted to the case of Dirichlet or Neumann boundary conditions. Although this problem does not initially possess the spectral gap property, it is shown that this property is satisfied after the proper non-local change of the dependent variable. The case of periodic boundary conditions where the situation is principally different and the inertial manifold may not exist is considered in the second part of our study.
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