On some autonomous nonlinear parabolic equations

Gary M. Lieberman

Iowa State University, USA

                        e-mail lieb@iastate.edu

There is a well-developed theory of nonlinear, second order parabolic equations with quite general coefficients. On the other hand, some recent work has been done for some special equations with time-independent coefficients. In this talk, we outline a general theory for such equations which is very close to the theory of elliptic equations. In particular, we show that some results of Altschuler and Wu on the evolution of surfaces by their mean curvature are valid in nonconvex domains.