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CarrilloVolume effects in the Keller-Segel model: energy estimates preventing blow-upJ. Subjects: Analysis of PDEs math. Which authors Kelle anal this paper are endorsers? Nonlinear Anal. The work is supported by the Russian Science Foundation under grant and performed in Petrozavodsk State University. Follow this author. New citations to this author. Laurent, and D. Upload PDF. Kelle anal Cuttas 3.

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### AMS :: Quarterly of Applied Mathematics

Abstract: We prove estimates on the densities that are obtained via the JKO scheme for a general form of a parabolic-elliptic Keller-Segel type system, with arbitrary diffusion, arbitrary mass, and in arbitrary dimension. Of course, such an estimate blows up in finite time, a time proportional to the inverse of the initial norm.

This estimate can be used to prove short-time well-posedness for a number of equations of this form regardless of the mass of the initial data. The time of existence of the constructed solutions coincides with the maximal time of existence of Lagrangian solutions without the diffusive term by characteristic methods.

References [Enhancements On Off] What's this? The work was finished during a visit of the second author to the Imperial College, in the framework of a joint CNRS-Imperial Fellowship; the hospitality and the financial support of the Imperial College are warmly acknowledged. MR [2] Luigi Ambrosio and Sylvia Serfaty , A gradient flow approach to an evolution problem arising in superconductivity , Comm.

Pure Appl. Paris , — French. MR [4] D. Carrillo , T. Laurent , and G. Raoul , Dimensionality of local minimizers of the interaction energy , Arch. Models Methods Appl. Carrillo , Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model , J. Partial Differential Equations 35 , no. Differential Equations , No. MR [12] L. Carrillo , Volume effects in the Keller-Segel model: energy estimates preventing blow-up , J.

Pures Appl. MR [17] J. Carrillo , M. DiFrancesco , A. Figalli , T. Laurent , and D. I Math. Convex Anal. MR [24] T. Hillen and K. Luckhaus , On explosions of solutions to a system of partial differential equations modelling chemotaxis , Trans. Keller and L. Segel, Initiation of slime mold aggregation viewed as an instability , J. Lisini, E.

Mainini and A. Segatti, A gradient flow approach to the porous medium equation with fractional pressure , Preprint arXiv Partial Differential Equations 26 , no. Calculus of variations, PDEs, and modeling. Old and new.

MR MR [2] Luigi Ambrosio and Sylvia Serfaty, A gradient flow approach to an evolution problem arising in superconductivity , Comm. Paris , French. Carrillo, T. Laurent, and G. Raoul, Dimensionality of local minimizers of the interaction energy , Arch. Carrillo, Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model , J.

Carrillo, Volume effects in the Keller-Segel model: energy estimates preventing blow-up , J. Carrillo, M. DiFrancesco, A. Figalli, T. Laurent, and D. Luckhaus, On explosions of solutions to a system of partial differential equations modelling chemotaxis , Trans.

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