Nonexistence Results for the Hyperbolic-Type Equations on Graded Lie Groups

Abstract

In this paper, we deal with systems of wave and pseudo-hyperbolic equations. Some semilinear equations for hypoelliptic operators on $${\mathbb {R}}^{n}$$ , Heisenberg groups, stratified Lie groups and graded Lie groups are studied. In particular, we obtain nonexistence results for nonlinear hyperbolic and pseudo-hyperbolic equations and systems on graded Lie groups. Also, we show Kato-type exponents for systems of pseudo-hyperbolic equations for Rockland operators on graded Lie groups.