Steady States with Jump Discontinuity in a Receptor-Based Model with Hysteresis in Higher-Dimensional Domains

.This paper deals with a receptor-based model which arises from the modeling of interactions between intracellular processes and diffusible signaling factors. We prove the existence of stationary solutions with jump discontinuity by a variational method. Then a singular perturbation problem with discontinuous nonlinearity is studied based on the patching argument and the implicit function theorem, to obtain a solution with a single transition layer. Moreover, we derive a sufficient condition for the stability of stationary solutions with jump discontinuity. In addition, some numerical simulations are presented to illustrate the theoretical results.Keywordsreceptor-based modeldiscontinuous patternshysteresistransition layersstabilityMSC codes35B3635K5735J4035B35