A NONLOCAL PARABOLIC EQUATION ARISING IN A TURBULENCE MODEL

We consider a class of parabolic partial differential equations with n onlocal diffusion coefficient. The study is motivated by a model of tu rbulent viscosity for a developed flow in a duct between parallel wall s. Under rather more general conditions, we use a rescaling in t to pr ove existence and well-posedness for weak solutions. Sharp comparison estimates enable us to bound from below the spatial derivative at the wall. The steady state problem is also nonstandard and we show local s tability by a spectral continuation argument. Finally numerical result s for the steady state solution are compared with available experiment al data. (C) 1997 Academic Press.