This paper deals with the study of the initial-boundary value problem of edge-hyperbolic system with damping term on the manifold with edge singularity. More precisely, it is analyzed the invariance and vacuum isolating of the solution sets to the edge-hyperbolic systems on edge Sobolev spaces. Then, by using a family of modified potential wells and concavity methods, it is obtained existence and nonexistence results of global solutions with exponential decay and is shown the blow-up in finite time of solutions on the manifold with edge singularities.
Semilinear hyperbolic equation, potential wells, cone Sobolev spaces, partial differential operator
KALLEJI, MORTEZA KOOZEHGAR and KADKHODA, NEMATOLLAH
"Vacuum isolating and blow-up analysis for edge hyperbolic system on edge Sobolev spaces,"
Turkish Journal of Mathematics: Vol. 44:
5, Article 29.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss5/29