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Sufficient conditions are obtained for the nonexistence of solutions to the nonlinear higher order pseudoparabolic equation utt −∆Hu+ (−∆H)u = f(η, t)u, (η, t) ∈ H× (0,∞), p > 1, u ≥ 0, where ∆H is 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. c ©2016 All rights reserved.

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