Optimal decay rate of solutions for nonlinear Klein-Gordon systems of critical type

Masaki, Satoshi; Sugiyama, Koki

doi:10.57262/die/1589594452

Cited by 1 publication

(4 citation statements)

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“…We show in Theorem 1.14 that the other two systems (1. 19) and (1.20) also admit a solution with the same kind of behavior. Further, Theorem 1.8 reveals that the system (1.7) is rather a limit case of (1.19).…”

Section: Theorem 11 For An Invertible Matrixmentioning

confidence: 77%

“…This is a unified notation of (1. 19) and (1.20). We use the unified notation because these two systems are handled quite similarly.…”

Section: Theorem 11 For An Invertible Matrixmentioning

confidence: 96%

“…Another difference is that the behavior of solutions to (1. 19) and (1.20) also involves a logarithmic phase correction. Theorem 1.16 suggests that the systems in Group 3 may admit a solution with a polynomial amplitude correction (see Remark 1.17).…”

Section: Theorem 11 For An Invertible Matrixmentioning

confidence: 99%

“…See [12,28] for the precise condition. In [19], the first author and Sugiyama showed that the dissipative decay rate is optimal in a class of systems. In particular, for any choice of coefficients of (1.1), there is no nontrivial classical solution which satisfies…”

Section: Introductionmentioning

confidence: 99%

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On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension

Masaki

Segata

Uriya

2022

Trans. Amer. Math. Soc. Ser. B

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In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Klein-Gordon equations in one space dimension. We classify the systems by studying the quotient set of a suitable subset of systems by the equivalence relation naturally induced by the linear transformation of the unknowns. It is revealed that the equivalence relation is well described by an identification with a matrix. In particular, we characterize some known systems in terms of the matrix and specify all systems equivalent to them. An explicit reduction procedure from a given system in the suitable subset to a model system, i.e., to a representative, is also established. The classification also draws our attention to some model systems which admit solutions with a new kind of asymptotic behavior. Especially, we find new systems which admit a solution of which decay rate is worse than that of a solution to the linear Klein-Gordon equation by logarithmic order.

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Section: Theorem 11 For An Invertible Matrixmentioning

confidence: 77%

“…This is a unified notation of (1. 19) and (1.20). We use the unified notation because these two systems are handled quite similarly.…”

Section: Theorem 11 For An Invertible Matrixmentioning

confidence: 96%

Section: Theorem 11 For An Invertible Matrixmentioning

confidence: 99%