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 utt−ΔHu+(−ΔH)δ2u=f(η;t)up;(η,t)∈H×(0,∞);p 1;u≥0; where Δ H is the Kohn{Laplace operator on the ( 2 N + 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.