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ArticleOriginal scientific text

Title

Nonlocal quadratic evolution problems

Authors 1, 2

Affiliations

  1. Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  2. Department of Statistics and Center for Stochastic and Chaotic Processes, in Science and Technology, Case Western Reserve University, Cleveland, Ohio 44106, U.S.A.

Abstract

Nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered. The inertial type nonlinearity is quadratic and nonlocal while the diffusive term, also nonlocal, is anomalous and fractal, i.e., represented by a fractional power of the Laplacian. Conditions for global in time existence versus finite time blow-up are studied. Self-similar solutions are constructed for certain homogeneous initial data. Monte Carlo approximation schemes by interacting particle systems are also mentioned.

Keywords

ENG
self-similar solutions, fractal anomalous diffusion, asymptotic behavior of solutions, nonlinear nonlocal parabolic equations

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Banach Center Publications
2000/52/1
Export to PBN, Opens in new tab
Pages:
11-24
Main language of publication
English
Published
2000
Exact and natural sciences