We discuss the asymptotic behavior of solutions for semilinear parabolic equations on the Heisenberg group with a singular potential. The singularity is controlled by Hardy's inequality, and the nonlinearity is controlled by Sobolev's inequality. We also establish the existence of a global branch of the corresponding steady states via the classical Rabinowitz theorem.
"Semilinear Parabolic Equations on the Heisenberg Group with a Singular Potential." Abstr. Appl. Anal. 2012 (SI12) 1 - 18, 2012. https://doi.org/10.1155/2012/749683