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In this paper, under suitable assumptions of the reaction term $F$ and the initial function $\\varphi$, we establish the method of obtaining higher order asymptotic expansions of the solution $u$ as $t\\to\\infty$. 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In this paper, under suitable assumptions of the reaction term $F$ and the initial function $\\varphi$, we establish the method of obtaining higher order asymptotic expansions of the solution $u$ as $t\\to\\infty$. 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