Hokkaido Mathematical Journal

KATAYAMA Soichiro,

Global existence and asymptotic behavior of solutions to systems of semilinear wave equations in two space dimensions.

Hokkaido Mathematical Journal, 37 (2008) pp.689-714

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Abstract

We consider the Cauchy problem for systems of semilinear wave equations in 2D with small initial data, and introduce a sufficient condition for global existence of small solutions. Our condition is weaker than the null condition for 2D wave equations, and it is motivated by Alinhac's condition for 3D. We also show that some global solutions under our condition are not asymptotically free.

MSC(Primary)35L70
MSC(Secondary)35L05, 35L15, 35B40
Uncontrolled Keywordssystem of nonlinear wave equations, null condition, weak null condition, grow-up of energy.