We consider the asymptotic behavior of solutions to the Cauchy problem for the defocusing nonlinear Klein-Gordon equation (NLKG) with exponential nonlinearity in the one spatial dimension with data in the energy space H-1 (R) x L-2 (R). We prove that any energy solution has a global bound of the L-t,x(6) space-time norm, and hence, scatters in H-1 (R) x L-2 (R) as t -> +/-infinity. The proof is based on the argument by Killip-Stovall-Visan (Trans. Amer. Math. Soc. 364(3) (2012) 1571-1631). However, since well-posedness in H-1/2 (R) x H-1/2 (R) for NLKG with the exponential nonlinearity holds only for small initial data, we use the (LtWx8-1/2,6)-W-6-norm for some s > 1/2 instead of the L-t,x(6)-norm, where W-x(8,p) denotes the sth order L-p-based Sobolev space.
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Univ Autonoma Chiapas, Fac Ciencias Fis & Matemat, Tuxtla Gutierrez 29050, Chiapas, MexicoUniv Autonoma Chiapas, Fac Ciencias Fis & Matemat, Tuxtla Gutierrez 29050, Chiapas, Mexico
Arceo, R.
Sandoval, L. M.
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Univ Autonoma Chiapas, Fac Ciencias Fis & Matemat, Tuxtla Gutierrez 29050, Chiapas, MexicoUniv Autonoma Chiapas, Fac Ciencias Fis & Matemat, Tuxtla Gutierrez 29050, Chiapas, Mexico
Sandoval, L. M.
Pedraza, Omar
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Univ Autonoma Estado Hidalgo, Area Acad Matemat & Fis, Carretera Pachuca Tulancingo Km 4-5, Mineral De La Reforma 42184, MexicoUniv Autonoma Chiapas, Fac Ciencias Fis & Matemat, Tuxtla Gutierrez 29050, Chiapas, Mexico
Pedraza, Omar
Lopez, L. A.
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Univ Autonoma Estado Hidalgo, Area Acad Matemat & Fis, Carretera Pachuca Tulancingo Km 4-5, Mineral De La Reforma 42184, MexicoUniv Autonoma Chiapas, Fac Ciencias Fis & Matemat, Tuxtla Gutierrez 29050, Chiapas, Mexico
Lopez, L. A.
Leon-Soto, G.
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Univ Michoacana, Ingn Energia & Sustentabilidad, Morelia 58030, Michoacan, MexicoUniv Autonoma Chiapas, Fac Ciencias Fis & Matemat, Tuxtla Gutierrez 29050, Chiapas, Mexico
Leon-Soto, G.
Martinez-Castro, J.
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Inst Politecn Nacl, Ctr Invest Comp, Ave Juan de Dios, Mexico City 07738, DF, MexicoUniv Autonoma Chiapas, Fac Ciencias Fis & Matemat, Tuxtla Gutierrez 29050, Chiapas, Mexico
Martinez-Castro, J.
INTERNATIONAL JOURNAL OF MODERN PHYSICS E,
2021,
30
(06):