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| 概要 |
The semilinear heat equation in the whole space R^n is considered, where the nonlinear terms are given as the forms ±|u|^κ or ±|u|^<κ−1_u>. In particular, we focus on global solutions for small initia...l data in L^<(κ−1)n/2>(R^n) under the conditions 1 + 2/n < κ < ∞ and κ /∈ N. We reveal that the global solutions have a regularity nearly C((0,∞);C^<κ+2>(R^n)). Moreover, by taking special initial data, we show that the global solutions do not belong to C^∞-class in space. From these results, we see that the space C^<κ+2>(R^n) may be regarded as a threshold of the regularity in space. The proof relies on the estimates of higher order derivatives of the nonlinear terms ±|u|^κ and ±|u|^<κ−1>u.続きを見る
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Mendeley出力
