Interactions of parabolic convective diffusion equations and Navier-Stokes equations connected with population dispersal (Q2782929)

The authors study the behaviour of the principal eigenvalue of indefinitely weighted parabolic eigenvalue problems with drift, subject to Dirichlet boundary conditions. The effects of weights and of various types of drifts on this eigenvalue are established. NEWLINENEWLINENEWLINEThen, the theory of convective diffusion equations is connected to that of Navier-Stokes equations, through the Hopf-Cole transformation. A control problem in the unit square initially formulated in the scope of stationary Navier-Stokes equations is treated in the framework of convective diffusion equations.