  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.
