Systems of reaction-diffusion equations with spatially distributed hysteresis

Pavel Gurevich; Sergey Tikhomirov

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 2, page 239-257
  • ISSN: 0862-7959

Abstract

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We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis on the right-hand side. The input of the hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic interaction of non-diffusive (bacteria, cells, etc.) and diffusive (nutrient, proteins, etc.) substances leading to formation of spatial patterns. We provide sufficient conditions under which the problem is well posed in spite of the assumed discontinuity of hysteresis. These conditions are formulated in terms of geometry of the manifolds defining the hysteresis thresholds and the spatial profile of the initial data.

How to cite

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Gurevich, Pavel, and Tikhomirov, Sergey. "Systems of reaction-diffusion equations with spatially distributed hysteresis." Mathematica Bohemica 139.2 (2014): 239-257. <http://eudml.org/doc/261916>.

@article{Gurevich2014,
abstract = {We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis on the right-hand side. The input of the hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic interaction of non-diffusive (bacteria, cells, etc.) and diffusive (nutrient, proteins, etc.) substances leading to formation of spatial patterns. We provide sufficient conditions under which the problem is well posed in spite of the assumed discontinuity of hysteresis. These conditions are formulated in terms of geometry of the manifolds defining the hysteresis thresholds and the spatial profile of the initial data.},
author = {Gurevich, Pavel, Tikhomirov, Sergey},
journal = {Mathematica Bohemica},
keywords = {spatially distributed hysteresis; reaction-diffusion equation; well-posedness; spatially distributed hysteresis; reaction-diffusion equation; well-posedness},
language = {eng},
number = {2},
pages = {239-257},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Systems of reaction-diffusion equations with spatially distributed hysteresis},
url = {http://eudml.org/doc/261916},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Gurevich, Pavel
AU - Tikhomirov, Sergey
TI - Systems of reaction-diffusion equations with spatially distributed hysteresis
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 2
SP - 239
EP - 257
AB - We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis on the right-hand side. The input of the hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic interaction of non-diffusive (bacteria, cells, etc.) and diffusive (nutrient, proteins, etc.) substances leading to formation of spatial patterns. We provide sufficient conditions under which the problem is well posed in spite of the assumed discontinuity of hysteresis. These conditions are formulated in terms of geometry of the manifolds defining the hysteresis thresholds and the spatial profile of the initial data.
LA - eng
KW - spatially distributed hysteresis; reaction-diffusion equation; well-posedness; spatially distributed hysteresis; reaction-diffusion equation; well-posedness
UR - http://eudml.org/doc/261916
ER -

References

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