演講訊息 TALKS

We consider the Cauchy problem for a semilinear parabolic equation with  a supercritical power nonlinearity.  It is known that the asymptotic behavior of solutions in time is determined by the decay rate of their initial values in space.  In particular, if an initial value decays like a radial steady state, then the corresponding solution converges to that steady state.  In this talk we consider solutions whose initial value decays in an anisotropic way.  Then we show that the solution converges to a steady state which is explicitly determined by an average formula.  The proof is given by using our previous results on the global stability and quasi-convergence of solutions, self-similar solutions of the linearized equation around a singular steady state, and a comparison technique.   This is a joint work with Peter Polacik of the University of Minnesota.