Stability properties of a heat equation with state-dependent parameters and asymmetric boundary conditions

Abstract

In this work the stability properties of a partial differential equation (PDE) with statedependent parameters and asymmetric boundary conditions are investigated. The PDE describes the temperature distribution inside foodstuff, but can also hold for other applications and phenomena. We show that the PDE converges to a stationary solution given by (fixed) boundary conditions which explicitly diverge from each other. Numerical simulations illustrate the results.