Blow-up of solutions with high energies of a coupled system of hyperbolic equations. (English) Zbl 1474.35460

Esquivel-Avila, Jorge A.

Abstr. Appl. Anal. 2019, Article ID 7405725, 11 p. (2019).

Summary: We consider an abstract coupled evolution system of second order in time. For any positive value of the initial energy, in particular for high energies, we give sufficient conditions on the initial data to conclude nonexistence of global solutions. We compare our results with those in the literature and show how we improve them.

MSC:

35L52	Initial value problems for second-order hyperbolic systems
35A01	Existence problems for PDEs: global existence, local existence, non-existence
35B44	Blow-up in context of PDEs
35L71	Second-order semilinear hyperbolic equations

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