PARABOLIC

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On the fractional doubly parabolic Keller-Segel system modelling chemotaxis
《Science China Mathematics》2022年第9期1827-1874,共48页Mario Bezerra Claudio Cuevas Clessius Silva Herme Soto 
supported by the National Research and Development Agency of Chile(ANID)-Chile under Fondecyt(Grant No.1181084)。
This work is concerned with the time-fractional doubly parabolic Keller-Segel system in R^(N)(N≥1),and we derive some refined results on the large time behavior of solutions which are presupposed to enjoy some unifor...
关键词：chemotaxis aggregation Keller-Segel model decay properties asymptotic profiles global solutions 
A finite dimensional proof of the Verlinde formula
《Science China Mathematics》2020年第10期1935-1964,共30页Xiaotao Sun Mingshuo Zhou 
supported by National Natural Science Foundation of China(Grant Nos.11831013 and 11921001);supported by National Natural Science Foundation of China(Grant No.11501154);Natural Science Foundation of Zhejiang Province(Grant No.LQ16A010005)。
We prove two recurrence relations among dimensions Dg(r,d,ω):=dim H^0(UC,ω,ΘUC,ω)of spaces of generalized theta functions on the moduli spaces UC,ω.By using these recurrence relations,an explicit formula(the Verl...
关键词：moduli space parabolic sheave generalized theta function Verlinde formula 
Hyperbolic-parabolic deformations of rational maps Dedicated to the Memory of Professor Lei Tan被引量：3
《Science China Mathematics》2018年第12期2157-2220,共64页Guizhen Cui Lei Tan 
supported by National Natural Science Foundation of China (Grant No. 11125106)
We develop a Thurston-like theory to characterize geometrically finite rational maps, and then apply it to study pinching and plumbing deformations of rational maps. We show that under certain conditions the pinching ...
关键词：rational map geometrically finite HYPERBOLIC PARABOLIC 
Variational minimizing parabolic and hyperbolic orbits for the restricted 3-body problems Dedicated to my Teacher Professor Yang Wannian on the Occasion of his 75th Birthday
《Science China Mathematics》2012年第4期721-725,共5页ZHANG ShiQing Department of Mathematics and Yangtze Center of Mathematics,Sichuan University,Chengdu 610064,China 
supported by National Natural Science Foundation of China (Grant No. 11071175);a grant for advisor and PhD students from educational committee of China
Using variational minimizing methods,we prove the existence of the odd symmetric parabolic or hyperbolic orbit for the restricted 3-body problems with weak forces.
关键词：restricted 3-body problems variational minimizers odd parabolic orbits odd hyperbolic orbits 
Compactness of the commutators of parabolic singular integrals被引量：8
《Science China Mathematics》2010年第10期2633-2648,共16页CHEN YanPing1 & DING Yong2,3 1Department of Mathematics and Mechanics,University of Science and Technology Beijing,Beijing 100083,China 2School of Mathematical Science,Beijing Normal University,Beijing 100875,China 3Laboratory of Mathematics and Complex Systems (BNU),Ministry of Education of China,Beijing 100875,China 
supported by National Natural Science Foundation of China (Grant Nos.10931001,10901017);Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20090003110018);Natural Science Foundation of Zhejiang Province (Grant No.Y7080325)
In this paper,the authors prove that the commutator [b,T] of the parabolic singular integrals is a compact operator on Lp(Rn)(1 < p < ∞) if and only if b ∈ VMO(Rn,ρ).The result is substantial improvement and ...
关键词：PARABOLIC singular INTEGRALS COMMUTATORS COMPACTNESS BMO VMO 
A new proof of L^p estimates for the parabolic polyharmonic equations被引量：1
《Science China Mathematics》2009年第4期749-756,共8页YAO FengPing ZHOU ShuLin 
supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905);Shang hai Leading Academic Discipline Project (Grant No. J50101);Key Disciplines of Shanghai Municipality (GrantNo. S30104);Zhou was supported by the National Basic Research Program of China (Grant No. 2006CB705700);National Natural Science Foundation of China (Grant No. 60532080);the Key Project of Chinese Ministryof Education (Grant No. 306017)
In this paper we obtain local Lp estimates for the parabolic polyharmonic equations by a straightforward approach.
关键词：polyharmonic PARABOLIC L p estimates 35K25 35G05 
A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations被引量：7
《Science China Mathematics》2008年第8期1376-1390,共15页CHEN YanPing HUANG YunQing YI NianYu 
the National Basic Research Program;the National Natural Science Foundation of China(Grant No.2005CB321703);Scientific Research Fund of Hunan Provincial Education Department;the Outstanding Youth Scientist of the National Natural Science Foundation of China(Grant No.10625106);the National Basic Research Program of China(Grant No.2005CB321701)
In this paper,we investigate the Legendre Galerkin spectral approximation of quadratic optimal control problems governed by parabolic equations.A spectral approximation scheme for the parabolic optimal control problem...
关键词：Legendre Galerkin spectral method optimal control problems parabolic state equations a posteriori error estimates 49J20 65M60 65M70 
Pseudo almost periodic solutions to parabolic boundary value inverse problems被引量：1
《Science China Mathematics》2008年第7期1203-1214,共12页ZHANG ChuanYi & YANG FengLin Department of Mathematics,Harbin Institute of Technology,Harbin 150001,China 
supported by the National Natural Science Foundation of China (Grant No. 10671046)
We first define the pseudo almost periodic functions in a more general setting.Then we show the existence,uniqueness and stability of pseudo almost periodic solutions of parabolic inverse problems for a type of bounda...
关键词：PSEUDO ALMOST periodic function INVERSE PROBLEM PARABOLIC equation boundary value PROBLEM 
Uniform blow-up profiles and boundary layer for a parabolic system with localized nonlinear reaction terms被引量：9
《Science China Mathematics》2005年第2期185-197,共13页LI Huiling & WANG Mingxin Department of Mathematics, Southeast University, Nanjing 210018, China Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, China 
This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditi...
关键词：PARABOLIC system  LOCALIZED nonlinear reaction terms  BLOW-UP profiles  boundary layer size. 
Self-similar solutions of quasilinear parabolic equations with nonlinear gradient terms
《Science China Mathematics》2004年第5期659-674,共16页SHI Peihu & WANG MingxinDepartment of Mathematics, Southeast University, Nanjing 210018, China Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, China 
This work was supported by the National Natural Science Foundation of China(Grant No.19831060);the"333"Project of Jiangsu Province.
This paper is devoted to study the classification of self-similar solutions to the quasilinear parabolic equations with nonlinear gradient termsu t = Δ(u m) - uq∣Δu∣ p withm ≥ 1,p,q > 0 andp +q >m. Form = 1, it i...
关键词：QUASILINEAR PARABOLIC equations  SELF-SIMILAR solutions  very SINGULAR solution  classification. 
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