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Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis. / Gurevich, P.; Tikhomirov, S.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 75, No. 18, 2012, p. 6610-6619.

Research output: Contribution to journal › Article

Harvard

Gurevich, P & Tikhomirov, S 2012, 'Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis', Nonlinear Analysis, Theory, Methods and Applications, vol. 75, no. 18, pp. 6610-6619. https://doi.org/10.1016/j.na.2012.08.003

APA

Gurevich, P., & Tikhomirov, S. (2012). Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis. Nonlinear Analysis, Theory, Methods and Applications, 75(18), 6610-6619. https://doi.org/10.1016/j.na.2012.08.003

Vancouver

Gurevich P, Tikhomirov S. Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis. Nonlinear Analysis, Theory, Methods and Applications. 2012;75(18):6610-6619. https://doi.org/10.1016/j.na.2012.08.003

Author

Gurevich, P. ; Tikhomirov, S. / Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis. In: Nonlinear Analysis, Theory, Methods and Applications. 2012 ; Vol. 75, No. 18. pp. 6610-6619.

BibTeX

@article{052596ffd1d44e3586f27bf327c23229,
title = "Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis",
abstract = "The paper deals with reaction–diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. Such problems describe biological processes and chemical reactions in which diffusive and nondiffusive substances interact according to hysteresis law. Under the assumption that the initial data are spatially transverse, we prove a theorem on the uniqueness of solutions. The theorem covers the case of non-Lipschitz hysteresis branches arising in the theory of slow–fast systems.",
keywords = "Spatially distributed hysteresis, Reaction–diffusion equation, Uniqueness of solution",
author = "P. Gurevich and S. Tikhomirov",
year = "2012",
doi = "10.1016/j.na.2012.08.003",
language = "English",
volume = "75",
pages = "6610--6619",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier",
number = "18",

}

RIS

TY - JOUR

T1 - Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis

AU - Gurevich, P.

AU - Tikhomirov, S.

PY - 2012

Y1 - 2012

N2 - The paper deals with reaction–diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. Such problems describe biological processes and chemical reactions in which diffusive and nondiffusive substances interact according to hysteresis law. Under the assumption that the initial data are spatially transverse, we prove a theorem on the uniqueness of solutions. The theorem covers the case of non-Lipschitz hysteresis branches arising in the theory of slow–fast systems.

AB - The paper deals with reaction–diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. Such problems describe biological processes and chemical reactions in which diffusive and nondiffusive substances interact according to hysteresis law. Under the assumption that the initial data are spatially transverse, we prove a theorem on the uniqueness of solutions. The theorem covers the case of non-Lipschitz hysteresis branches arising in the theory of slow–fast systems.

KW - Spatially distributed hysteresis

KW - Reaction–diffusion equation

KW - Uniqueness of solution

U2 - 10.1016/j.na.2012.08.003

DO - 10.1016/j.na.2012.08.003

M3 - Article

VL - 75

SP - 6610

EP - 6619

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 18

ER -

ID: 5467275