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Volumn 32, Issue 1, 2009, Pages 112-126

Two-dimensional chemotaxis models with fractional diffusion

Author keywords

Besov spaces; Chemotaxis model; Fractional diffusion; Local existence of solutions

Indexed keywords

BANACH SPACES; DIFFUSION; FOURIER ANALYSIS; FOURIER TRANSFORMS; PROGRAMMING THEORY;

EID: 58449099055     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.1036     Document Type: Article
Times cited : (68)

References (27)
  • 1
    • 0000657461 scopus 로고    scopus 로고
    • Local and global solvability of parabolic systems modelling chemotaxis
    • Biler P. Local and global solvability of parabolic systems modelling chemotaxis. Advances in Mathematical Sciences and Applications 1998; 8:715-743.
    • (1998) Advances in Mathematical Sciences and Applications , vol.8 , pp. 715-743
    • Biler, P.1
  • 2
    • 11144305807 scopus 로고    scopus 로고
    • Global regular and singular solutions for a model of gravitating particles
    • Biler P, Cannone M, Guerra I, Karch G. Global regular and singular solutions for a model of gravitating particles. Mathematische Annalen 2004; 330:693-708.
    • (2004) Mathematische Annalen , vol.330 , pp. 693-708
    • Biler, P.1    Cannone, M.2    Guerra, I.3    Karch, G.4
  • 3
    • 0345504868 scopus 로고    scopus 로고
    • Global and exploding solutions for nonlocal quadratic evolution problems
    • Biler P, Woyczyński WA. Global and exploding solutions for nonlocal quadratic evolution problems. SIAM Journal on Applied Mathematics 1998; 59:845-869.
    • (1998) SIAM Journal on Applied Mathematics , vol.59 , pp. 845-869
    • Biler, P.1    Woyczyński, W.A.2
  • 5
    • 58449126476 scopus 로고    scopus 로고
    • Karch G. Scaling in nonlinear parabolic equations: applications to Debye system (in English). In Proceedings of the International Conference on Disordered and Complex Systems, London, U.K., 10-14 July 2000, Sollich P et al. (eds). American Institute of Physics: Melville, NY (AIP Conference Proceedings 2001; 553:243-248).
    • Karch G. Scaling in nonlinear parabolic equations: applications to Debye system (in English). In Proceedings of the International Conference on Disordered and Complex Systems, London, U.K., 10-14 July 2000, Sollich P et al. (eds). American Institute of Physics: Melville, NY (AIP Conference Proceedings 2001; 553:243-248).
  • 7
    • 4644223876 scopus 로고    scopus 로고
    • Time-space estimates of solutions to general semilinear parabolic equations
    • Miao C. Time-space estimates of solutions to general semilinear parabolic equations. Tokyo Journal of Mathematics 2001; 24:245-276.
    • (2001) Tokyo Journal of Mathematics , vol.24 , pp. 245-276
    • Miao, C.1
  • 8
    • 4644298299 scopus 로고    scopus 로고
    • Space-time estimates for parabolic type operator and application to nonlinear parabolic equations
    • Miao C, Gu Y. Space-time estimates for parabolic type operator and application to nonlinear parabolic equations. Journal of Partial Differential Equations 1998; 11:301-312.
    • (1998) Journal of Partial Differential Equations , vol.11 , pp. 301-312
    • Miao, C.1    Gu, Y.2
  • 9
    • 4644283096 scopus 로고    scopus 로고
    • The Cauchy problem for semilinear parabolic equations in Besov spaces
    • Miao C, Zhang B. The Cauchy problem for semilinear parabolic equations in Besov spaces. Houston Journal of Mathematics 2004; 30:829-878.
    • (2004) Houston Journal of Mathematics , vol.30 , pp. 829-878
    • Miao, C.1    Zhang, B.2
  • 10
    • 33846038745 scopus 로고    scopus 로고
    • The fractional Keller-Segel model
    • Escudero C. The fractional Keller-Segel model. Nonlinearity 2006; 19:2909-2918.
    • (2006) Nonlinearity , vol.19 , pp. 2909-2918
    • Escudero, C.1
  • 11
    • 27244457542 scopus 로고    scopus 로고
    • Chemotactic collapse and mesenchymal morphogenesis
    • Escudero C. Chemotactic collapse and mesenchymal morphogenesis. Physical Review E 2005; 72:022903.
    • (2005) Physical Review E , vol.72 , pp. 022903
    • Escudero, C.1
  • 12
    • 0009978417 scopus 로고
    • Existence and nonexistence of solutions for a model of gravitational interaction of particles III
    • Biler P. Existence and nonexistence of solutions for a model of gravitational interaction of particles III. Colloquium Mathematicum 1995; 68:229-239.
    • (1995) Colloquium Mathematicum , vol.68 , pp. 229-239
    • Biler, P.1
  • 13
    • 34247507199 scopus 로고    scopus 로고
    • General nonlocal diffusion-convection mean field models: Nonexistence of global solutions
    • Biler P, Woyczyński WA. General nonlocal diffusion-convection mean field models: nonexistence of global solutions. Physica A 2007; 379:523-533.
    • (2007) Physica A , vol.379 , pp. 523-533
    • Biler, P.1    Woyczyński, W.A.2
  • 14
    • 58449116481 scopus 로고    scopus 로고
    • Blow up of solutions of nonlinear evolution equations with Lévy diffusion operators
    • In preparation
    • Biler P, Karch G. Blow up of solutions of nonlinear evolution equations with Lévy diffusion operators. In preparation.
    • Biler, P.1    Karch, G.2
  • 15
    • 58449088604 scopus 로고    scopus 로고
    • 2. Preprint arXiv: math.AP/0712.3169v1, 2007; 1-26.
    • 2. Preprint arXiv: math.AP/0712.3169v1, 2007; 1-26.
  • 16
    • 0037144962 scopus 로고    scopus 로고
    • Self-similar solutions to a parabolic system modeling chemotaxis
    • Naito Y, Suzuki T, Yoshida K. Self-similar solutions to a parabolic system modeling chemotaxis. Journal of Differential Equations 2002; 184:386-421.
    • (2002) Journal of Differential Equations , vol.184 , pp. 386-421
    • Naito, Y.1    Suzuki, T.2    Yoshida, K.3
  • 17
    • 58149493159 scopus 로고    scopus 로고
    • Asymptotically self-similar solutions for the parabolic systems modelling chemotaxis
    • Banach Center Publications, Polish Academy of Sciences: Warsaw
    • Naito Y. Asymptotically self-similar solutions for the parabolic systems modelling chemotaxis. Self-similar Solutions in Nonlinear PDE, vol. 74. Banach Center Publications, Polish Academy of Sciences: Warsaw, 2006; 149-160.
    • (2006) Self-similar Solutions in Nonlinear PDE , vol.74 , pp. 149-160
    • Naito, Y.1
  • 18
    • 58449134715 scopus 로고    scopus 로고
    • A note on the paper of Y. Naito
    • Banach Center Publications, Polish Academy of Sciences: Warsaw
    • Biler P. A note on the paper of Y. Naito. Self-similar Solutions in Nonlinear PDE, vol. 74. Banach Center Publications, Polish Academy of Sciences: Warsaw, 2006; 33-40.
    • (2006) Self-similar Solutions in Nonlinear PDE , vol.74 , pp. 33-40
    • Biler, P.1
  • 21
    • 38049069749 scopus 로고    scopus 로고
    • Well-posedness of the Cauchy problem for the fractional power dissipative equation in critical Besov spaces
    • Wu G, Yuan J. Well-posedness of the Cauchy problem for the fractional power dissipative equation in critical Besov spaces. Journal of Mathematical Analysis and Applications 2008; 340:1326-1335.
    • (2008) Journal of Mathematical Analysis and Applications , vol.340 , pp. 1326-1335
    • Wu, G.1    Yuan, J.2
  • 23
    • 0038205255 scopus 로고    scopus 로고
    • Perfect Incompressible Fluids
    • The Clarendon Press, Oxford University Press: New York
    • Chemin J-Y. Perfect Incompressible Fluids. Oxford Lecture Series in Mathematics and its Applications, vol. 14. The Clarendon Press, Oxford University Press: New York, 1998.
    • (1998) Oxford Lecture Series in Mathematics and its Applications , vol.14
    • Chemin, J.-Y.1
  • 25
    • 67649574180 scopus 로고    scopus 로고
    • Harmonic analysis tools for solving the incompressible Navier-Stokes equations
    • Friedlander SJ, Serre D eds, Elsevier: Amsterdam
    • Cannone M. Harmonic analysis tools for solving the incompressible Navier-Stokes equations. In Handbook of Mathematical Fluid Dynamics, vol. III, Friedlander SJ, Serre D (eds). Elsevier: Amsterdam, 2004; 161-244.
    • (2004) Handbook of Mathematical Fluid Dynamics , vol.3 , pp. 161-244
    • Cannone, M.1
  • 26
    • 33846524186 scopus 로고    scopus 로고
    • Solutions to some nonlinear parabolic equations in pseudomeasure spaces
    • Miao C, Yuan B. Solutions to some nonlinear parabolic equations in pseudomeasure spaces. Mathematische Nachrichten 2007; 280:171-186.
    • (2007) Mathematische Nachrichten , vol.280 , pp. 171-186
    • Miao, C.1    Yuan, B.2
  • 27
    • 58149496471 scopus 로고    scopus 로고
    • Stability property of the two-dimensional Keller-Segel model, 1-30
    • in press
    • Raczyński A. Stability property of the two-dimensional Keller-Segel model, 1-30. Asymptotic Analysis, in press.
    • Asymptotic Analysis
    • Raczyński, A.1


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