具有大扩散和对流边界加热的反应扩散方程半流的庞加莱紧化
Poincaré compactification for semiflows of reaction-diffusion equations with large diffusion and convection heating at the boundary
AI总结：
本文对具有大扩散和边界对流加热的耦合PDE-ODE系统极限半流进行庞加莱紧化，利用不变流形定理降维，并证明紧化向量场在C^1范数下接近。
摘要：
本文研究了一个由反应扩散方程（具有大扩散）与常微分方程通过加热过渡区域中的边界条件耦合而成的PDE-ODE系统的极限平面半流的庞加莱紧化。非线性源项为耗散多项式。我们保证了应用不变流形定理的条件，以降低偏微分方程的维数，并证明了紧化向量场在$C^1$-范数下是接近的。
英文摘要：
In this paper, we study the Poincaré compactification of the limiting planar semiflow of a coupled PDE-ODE system composed by a reaction-diffusion equation with large diffusion coupled with an ODE by a boundary condition in a heating transition region. The nonlinear sources are dissipative polynomials. We guarantee conditions to apply the Invariant Manifold Theorem in order to reduce the dimension of the PDE and we prove that the compactified vector fields are close in the $C^1$-norm.
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