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Remark on the Cauchy problem for the evolution p-Laplacian equation
Liangwei Wang1, Jngxue Yin2, Jinde Cao3
1School of Mathematics and Statistics, Chongqing Three Gorges University, No. 666, Tian Xing Road, Wanzhou District, Chongqing, 404100 China.
Abstract:
In this paper, we prove that the semigroup [Formula: see text] generated by the Cauchy problem of the evolution p-Laplacian equation [Formula: see text] ([Formula: see text]) is continuous form a weighted [Formula: see text] space to the continuous space [Formula: see text]. Then we use this property to reveal the fact that the evolution p-Laplacian equation generates a chaotic dynamical system on some compact subsets of [Formula: see text]. For this purpose, we need to establish the propagation estimates and the space-time decay estimates for the solutions first.
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