Department of Mathematics2024-11-0920181534-039210.3934/cpaa.20180482-s2.0-85044411854http://dx.doi.org/10.3934/cpaa.2018048https://hdl.handle.net/20.500.14288/14761We consider the Cauchy problem for nonlinear abstract wave equations in a Hilbert space. Our main goal is to show that this problem has solutions with arbitrary positive initial energy that blow up in a finite time. The main theorem is proved by employing a result on growth of solutions of abstract nonlinear wave equation and the concavity method. A number of examples of nonlinear wave equations are given. A result on blow up of solutions with arbitrary positive initial energy to the initial boundary value problem for the wave equation under nonlinear boundary conditions is also obtained.MathematicsApplied mathematicsJournal Article1553-5258439236400011967