In this article, we study the Poincaré compactification of the limiting planar semiflow of a coupled partial differential equation and ordinary differential equation system composed of a reaction–diffusion equation with large diffusion coupled with an ordinary differential equation 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 partial differential equation and prove that the compactified vector fields are close in the -norm.
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