Nonlocal quadratic evolution problems

Piotr Biler; Wojbor Woyczyński

Banach Center Publications (2000)

  • Volume: 52, Issue: 1, page 11-24
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Biler, Piotr, and Woyczyński, Wojbor. "Nonlocal quadratic evolution problems." Banach Center Publications 52.1 (2000): 11-24. <http://eudml.org/doc/209050>.

@article{Biler2000,
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.},
author = {Biler, Piotr, Woyczyński, Wojbor},
journal = {Banach Center Publications},
keywords = {self-similar solutions; fractal anomalous diffusion; asymptotic behavior of solutions; nonlinear nonlocal parabolic equations; evolution of density of mutually interacting particles; fractional power of the Laplacian; global in time existence versus finite time blow-up; Monte Carlo approximation schemes},
language = {eng},
number = {1},
pages = {11-24},
title = {Nonlocal quadratic evolution problems},
url = {http://eudml.org/doc/209050},
volume = {52},
year = {2000},
}

TY - JOUR
AU - Biler, Piotr
AU - Woyczyński, Wojbor
TI - Nonlocal quadratic evolution problems
JO - Banach Center Publications
PY - 2000
VL - 52
IS - 1
SP - 11
EP - 24
AB - 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.
LA - eng
KW - self-similar solutions; fractal anomalous diffusion; asymptotic behavior of solutions; nonlinear nonlocal parabolic equations; evolution of density of mutually interacting particles; fractional power of the Laplacian; global in time existence versus finite time blow-up; Monte Carlo approximation schemes
UR - http://eudml.org/doc/209050
ER -

References

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