کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898708 | 1631495 | 2018 | 53 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Cauchy problems for Keller-Segel type time-space fractional diffusion equation
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
This paper investigates Cauchy problems for nonlinear fractional time-space generalized Keller-Segel equation Dtβ0cÏ+(ââ³)α2Ï+ââ
(ÏB(Ï))=0, where Caputo derivative Dtβ0cÏ models memory effects in time, fractional Laplacian (ââ³)α2Ï represents Lévy diffusion and B(Ï)=âsn,γâ«Rnxây|xây|nâγ+2Ï(y)dy is the Riesz potential with a singular kernel which takes into account the long rang interaction. We first establish LrâLq estimates and weighted estimates of the fundamental solutions (P(x,t),Y(x,t)) (or equivalently, the solution operators (Sαβ(t),Tαβ(t))). Then, we prove the existence and uniqueness of the mild solutions when initial data are in Lp spaces, or the weighted spaces. Similar to Keller-Segel equations, if the initial data are small in critical space Lpc(Rn) (pc=nα+γâ2), we construct the global existence. Furthermore, we prove the L1 integrability and integral preservation when the initial data are in L1(Rn)â©Lp(Rn) or L1(Rn)â©Lpc(Rn). Finally, some important properties of the mild solutions including the nonnegativity preservation, mass conservation and blowup behaviors are established.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 265, Issue 3, 5 August 2018, Pages 1044-1096
Journal: Journal of Differential Equations - Volume 265, Issue 3, 5 August 2018, Pages 1044-1096
نویسندگان
Lei Li, Jian-Guo Liu, Lizhen Wang,