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Large time behavior of solutions to semilinear systems of wave equations. (English) Zbl 1114.35129
The authors study asymptotic behavior of radially symmetric solutions of the initial value problem to the coupled wave equations \[ u_{tt}-c_1\triangle u=| v_t| ^p,\;v_{tt}-c_2\triangle v=| u_t| ^q, \;t>0, \;x\in \mathbb{R}^3. \] Under some conditions, they find small global solution of the problem and prove its convergence to a modified “free profile”. Moreover, they find some conditions, for which a global solution cannot exist.

MSC:
35L70 Second-order nonlinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
35L15 Initial value problems for second-order hyperbolic equations
35L55 Higher-order hyperbolic systems
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