Blow-Up Phenomena for Gradient Flows of Discrete Homogeneous Functionals View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-04

AUTHORS

Vincent Calvez, Thomas O. Gallouët

ABSTRACT

We investigate gradient flows of some homogeneous functionals in RN, arising in the Lagrangian approximation of systems of self-interacting and diffusing particles. We focus on the case of negative homogeneity. In the case of strong self-interaction (super critical case), the functional possesses a cone of negative energy. It is immediate to see that solutions with negative energy at some time become singular in finite time, meaning that a subset of particles concentrate at a single point. Here, we establish that all solutions become singular in finite time, in the super critical case, for the class of functionals under consideration. The paper is completed with numerical simulations illustrating the striking non linear dynamics when initial data have positive energy. More... »

PAGES

453-481

References to SciGraph publications

  • 2009-06. Critical mass for a Patlak–Keller–Segel model with degenerate diffusion in higher dimensions in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 2009-01. A user’s guide to PDE models for chemotaxis in JOURNAL OF MATHEMATICAL BIOLOGY
  • 2009. Optimal Transport, Old and New in NONE
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    http://scigraph.springernature.com/pub.10.1007/s00245-017-9443-z

    DOI

    http://dx.doi.org/10.1007/s00245-017-9443-z

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1091602490


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