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Asymptotic dynamics for reaction diffusion equations in unbounded domain
Keywords:Reaction diffusion equation, semigroup, exponential attractor.
Abstract:
      In this paper we study the asymptotic dynamics for reaction diffusion equation defined in $\mathbb{R}^n$. We will prove that the equation possesses a fixed point when the nonlinearity satisfies some restrictive conditions and then we show that the fixed point is an exponential attractor.