On hysteresis–reaction–diffusion systems: Singular fast-reaction limit derivation and nonlinear hysteresis feedback

This paper concerns a general class of PDE-ODE reaction-diffusion systems, which features singular fast-reaction limit towards equation coupled to scalar hysteresis operator. As prototypical application, we present PDE model for the growth population according given food supply an ODE turnover stock. Under realistic conditions stock is much faster than yielding intrinsic scaling parameter. We two models consume rate functions such that resulting dynamics converges generalised play operator in associated fast-reaction-limit. emphasise structural assumptions on considered are quite and analogue systems might describe e.g. cell-biological buffer mechanisms, where proteins stored used parallel. Finally, discuss explicit example showing nonlinear coupling with can lead spatially inhomogeneous large-time behaviour kind hysteresis-diffusion driven instability.