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Fractional diffusion with two time scales

✍ Scribed by B. Baeumer; M.M. Meerschaert

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
253 KB
Volume
373
Category
Article
ISSN
0378-4371

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## Abstract In this paper we study the Cauchy problem for the fractional diffusion equation __u__~__t__~ + (βˆ’Ξ”)^Ξ±/2^__u__=βˆ‡Β·(__u__βˆ‡(Ξ”^βˆ’1^__u__)), generalizing the Keller–Segel model of chemotaxis, for the initial data __u__~0~ in critical Besov spaces __αΈ‚__(ℝ^2^) with __r__∈[1, ∞], where 1<Ξ±<2. Mak