Nonexistence of global weak solutions of a system of wave equations on the Heisenberg group

Sufficient conditions are obtained for the nonexistence of solutions to the nonlinear higher order pseudoparabolic equation u_tt–Δ_ℍ^u+ (–Δℍ)^δ/2u= f(η, t)u^p; (η, t) ϵ ℍ × (0,∞); p > 1, u ≥ 0; where Δ_ℍis the Kohn-Laplace operator on the (2N + 1)-dimensional Heisenberg group ℍ and f(η, t) is a given function. Then, this result is extended to the case of a 2 × 2-system of the same type. Our technique of proof is based on a duality argument.