Large time behavior of solutions to the nonlinear heat equation with absorption

In this talk, we study global well-posedness and long time asymptotic behavior of solutions to the nonlinear heat equation with absorption. We focus particularly on highly singular initial values which are antisymmetric with respect to some variables. Our approach is to study well-posedness and large time behavior on sectorial domains, and then to extend the results by reflection to solutions on the whole space which are antisymmetric. Our results include, among others, new examples of self-similar and asymptotically self-similar solutions. This is a joint work with Hattab Mouajria and Fred B. Weissler.