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Generalized wave operators for a system of semilinear wave equations in three space dimensions. (English) Zbl 1272.35140
The authors studied extensively the final value problem for a system of semilinear wave equations. The main issue is to solve the problem when the nonlinearity is of a long-range type. By assuming that the solution is spherically symmetric, they have proved that the global solvability of the final value problem around a suitable final state, and hence, explained the methodology of constructing the generalized wave operator and long range-scattering operator.
35L51 Second-order hyperbolic systems
35L70 Second-order nonlinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
35L71 Second-order semilinear hyperbolic equations
Full Text: DOI Euclid