Hokkaido Mathematical Journal

KUBO Hideo, KUBOTA Kôji,

Generalized wave operators for a system of semilinear wave equations in three space dimensions.

Hokkaido Mathematical Journal, 42 (2013) pp.81-111

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Abstract

This paper is concerned with 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, we shall show global solvability of the final value problem around a suitable final state, and hence, the generalized wave operator and long range-scattering operator can be constructed.

MSC(Primary)35L70
MSC(Secondary)35B40
Uncontrolled KeywordsFinal value problem, system of semilinear wave equations, generalized wave operator, long-range scattering operator