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Then we apply it to study the classical Keller-Segel system \\begin{equation} \\left\\{ \\begin{array}{llc} u_t=\\Delta u-\\nabla\\cdot(u \\nabla v), \\\\[6pt] \\displaystyle v_t=\\Delta v-v+u, \\end{array} \\right. \\end{equation} in a bounded domain $\\Omega\\subset\\mathbb{R}^N$ ($N\\ge 2$) with smooth boundary. 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