Asymptotic behavior of solutions to semilinear systems of wave equations Soichiro KatayamaHideo Kubo 35L7035B40grow-up of energysystem of nonlinear wave equationsnull conditionweak null condition We consider the Cauchy problem for a class of systems of semilinear wave equations, which is closely connected to the weak null condition and Alinhac's condition. We show that the energy of some global solutions to these systems grows to infinity as time tends to infinity and consequently these solutions never approach any free solutions. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3166 10.1512/iumj.2008.57.3166 en Indiana Univ. Math. J. 57 (2008) 377 - 400 state-of-the-art mathematics http://iumj.org/access/