Upper, Lower Solutions and Analytic Semigroups For a Model with Diffusion

In this discussion we consider an autonomous parabolic epidemic 2-dimensional system modelling the dynamics of transmission of immunizing diseases for a closed population into bounded regular domain. Our model takes into account diffusion of population with external influx as well as one class of infected individuals. We study the well-posedness two-component diffusion equations including external supplies with Neumann conditions using upper/lower solutions and analytic semigroups. In case of constant population or not, with non-oscillatory solution and constant diffusion, this problem admits travelling wave solutions whose minimum wave speed is surveyed here