Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).
Том 8136 LNCS.
2013.
С. 369-380
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.