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Semilinear parabolic equations on the Heisenberg group with a singular potential. (English) Zbl 1242.35149

Summary: 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.

MSC:

35K58 Semilinear parabolic equations
35R03 PDEs on Heisenberg groups, Lie groups, Carnot groups, etc.
35B40 Asymptotic behavior of solutions to PDEs
35K67 Singular parabolic equations
35B32 Bifurcations in context of PDEs
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