Global existence and asymptotic behavior of solutions to a semilinear parabolic equation on Carnot groups

Abstract

In this paper we consider the semilinear parabolic equationj is a positive definite symmetric matrix and the X i 's denotes a system of left-invariant vector fields on a Carnot group G. Based on a fixed point argument and by establishing some new estimates involving the heat kernel, we study the existence and large-time behavior of global positive solutions to the preceding equation. MSC: 35K65; 35J70; 35B40