Nonexistence results for a class of evolution equations in the Heisenberg group

We establish a nonexistence result of global solutions to the nonlinear evolution equation (eqution presented) where Δℍ is the Kohn-Laplace operator on the (2N+1)-dimensional Heisenberg group H, |v|_ℍ is the distance from v to the origin, β, p, q > 0, α ≥ 0, f(t, v) ≥ 0, h(v) and w(t, v) are given functions. Next, we extend this result to the case of systems. Our technique of proof is based on Pohozaev's nonlinear capacity method.