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Then, we show the asymptotic behavior and regularizing-decay rate estimates of the solution to equations with power-law nonlinearity by the method of multi-linear operator and the classical Hardy-Littlewood-Sobolev inequality.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.2023005","type":"journal-article","created":{"date-parts":[[2022,11,17]],"date-time":"2022-11-17T08:56:13Z","timestamp":1668675373000},"page":"109-139","source":"Crossref","is-referenced-by-count":5,"title":["Global solution to the Cauchy problem of fractional drift diffusion system with power-law nonlinearity"],"prefix":"10.3934","volume":"18","author":[{"given":"Caihong","family":"Gu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China"}]},{"given":"Yanbin","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China"},{"name":"Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2023005-1","doi-asserted-by":"crossref","unstructured":"N. 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