【摘 要】
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We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension. On the one hand, by Banach fixed point theorem and some properties of heat kernel, we prove the local existence and the global
【机 构】
：
College of Science,Donghua University,Shanghai 201620,China
论文部分内容阅读
We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension. On the one hand, by Banach fixed point theorem and some properties of heat kernel, we prove the local existence and the global existence of integral solutions for the different initial data under some conditions that involve the size of the initial data. On the other hand, in the case of global solutions, we obtain their optimal time decay by Gronwall\'s lemma.
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