Reaction-diffusion equations with spatially distributed hysteresis

This paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which diffusive and nondiffusive substances interact according to hysteresis law. We find sufficient conditions that guarantee the existence and uniqueness of solutions as well as their continuous dependence on initial data. © 2013 Society for Industrial and Applied Mathematics.

Authors
Gurevich P. 1, 2 , Shamin R.3 , Tikhomirov S.1
Number of issue
3
Language
English
Pages
1328-1355
Status
Published
Volume
45
Year
2013
Organizations
  • 1 Mathematical Institute i, Free University of Berlin, Berlin 14195, Germany
  • 2 Peoples' Friendship University of Russia, Russian Federation
  • 3 Institute of Marine Geology and Geophysics, Russian Academy of Sciences-Far Eastern Branch, Yuzhno-Sakhalinsk 693022, Russian Federation
Keywords
Reaction-diffusion equation; Spatially distributed hysteresis; Well-posedness
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/1990/
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