Diffusion with resetting in bounded domains

We consider the one-dimensional diffusion in a bounded domain with stochastic resetting. We start our analysis by presenting a method to derive the master equation for different resetting mechanisms. In the next step we compute the non-equilibrium steady state for a special case of this differential equation. Then we consider the existence of an absorbing point in the system and calculate the mean time to absorption of the diffusive particle by the target. Numerical and analytical calculations of the optimal resetting rate reveal a second order phase transition. Finally we discuss different special cases of the presented problem.