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

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. © 2012 Elsevier Ltd. All rights reserved.

Authors
Gurevich P. 1, 2 , Tikhomirov S.1
Publisher
Elsevier Ltd
Number of issue
18
Language
English
Pages
6610-6619
Status
Published
Volume
75
Year
2012
Organizations
  • 1 Free University of Berlin, Germany
  • 2 Peoples' Friendship University of Russia, Russian Federation
Keywords
Reaction-diffusion equation; Spatially distributed hysteresis; Uniqueness of solution
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/2215/
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