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Systems of reaction-diffusion equations with spatially distributed hysteresis. / Gurevich, Pavel; Tikhomirov, Sergey.

In: Mathematica Bohemica, Vol. 139, No. 2, 2014, p. 239-257.

Research output: Contribution to journal › Article › peer-review

Harvard

Gurevich, P & Tikhomirov, S 2014, 'Systems of reaction-diffusion equations with spatially distributed hysteresis', Mathematica Bohemica, vol. 139, no. 2, pp. 239-257. <http://mb.math.cas.cz/mb139-2/11.html>

APA

Gurevich, P., & Tikhomirov, S. (2014). Systems of reaction-diffusion equations with spatially distributed hysteresis. Mathematica Bohemica, 139(2), 239-257. http://mb.math.cas.cz/mb139-2/11.html

Vancouver

Gurevich P, Tikhomirov S. Systems of reaction-diffusion equations with spatially distributed hysteresis. Mathematica Bohemica. 2014;139(2):239-257.

Author

Gurevich, Pavel ; Tikhomirov, Sergey. / Systems of reaction-diffusion equations with spatially distributed hysteresis. In: Mathematica Bohemica. 2014 ; Vol. 139, No. 2. pp. 239-257.

BibTeX

@article{1534f78b250d4187b528a4be19f80a26,
title = "Systems of reaction-diffusion equations with spatially distributed hysteresis",
abstract = "We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of 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 discontinuity of hysteresis. These conditions are formulated in terms of geometry of manifolds defining hysteresis thresholds and the graph of initial data.",
keywords = "spatially-distributed hysteresis, reaction-diffusion equation, well-posedness.",
author = "Pavel Gurevich and Sergey Tikhomirov",
year = "2014",
language = "English",
volume = "139",
pages = "239--257",
journal = "Mathematica Bohemica",
issn = "0862-7959",
publisher = "Czech Academy of Sciences",
number = "2",

}

RIS

TY - JOUR

T1 - Systems of reaction-diffusion equations with spatially distributed hysteresis

AU - Gurevich, Pavel

AU - Tikhomirov, Sergey

PY - 2014

Y1 - 2014

N2 - We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of 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 discontinuity of hysteresis. These conditions are formulated in terms of geometry of manifolds defining hysteresis thresholds and the graph of initial data.

AB - We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of 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 discontinuity of hysteresis. These conditions are formulated in terms of geometry of manifolds defining hysteresis thresholds and the graph of initial data.

KW - spatially-distributed hysteresis

KW - reaction-diffusion equation

KW - well-posedness.

M3 - Article

VL - 139

SP - 239

EP - 257

JO - Mathematica Bohemica

JF - Mathematica Bohemica

SN - 0862-7959

IS - 2

ER -

ID: 5726064