Blow-up solutions of damped Klein-Gordon equation on the Heisenberg group

Abstract

Inthisnote,weprovetheblow-upofsolutionsofthesemilineardamped Klein-Gordon equation in a finite time for arbitrary positive initial energy on the Heisenberg group. This work complements the paper [21] by the first author and Tokmagambetov, where the global in time well-posedness was proved for the small energy solutions.

References in corpus (5)

• Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups
• Sharp $L^p$-bounds for the wave equation on groups of Heisenberg type
• Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity
• Decay estimates for the linear damped wave equation on the Heisenberg group
• Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified Groups

Cited by in corpus (1)

• Instantaneous blow up solutions for nonlinear Sobolev type equations on the Heisenberg Group