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作者:Nakao Hayashi , Elena I. Kaikina
来源:[J].Nonlinear Analysis(IF 1.64), 2019, Vol.187, pp.279-306
摘要:Abstract(#br)We consider the inhomogeneous Dirichlet-boundary value problem for nonlinear Schrödinger equations with a power nonlinearity in the upper half plane. We present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solution...
作者:Nakao Hayashi , Pavel I. Naumkin
来源:[J].Journal of Mathematical Analysis and Applications(IF 1.05), 2017, Vol.446 (1), pp.801-822
摘要:Abstract(#br)We study the Cauchy problem for nonlinear damped wave equations with a critical defocusing power nonlinearity | u | 2 n u , where n denotes the space dimension. For n = 1 , 2 , 3 , global in time existence of small solutions was shown in [4]. In this paper, we genera...
作者:Liliana Esquivel , Nakao Hayashi , Elena I. Kaikina
来源:[J].Journal of Differential Equations(IF 1.48), 2018
摘要:Abstract(#br)We consider the inhomogeneous Dirichlet-boundary value problem for the cubic nonlinear Schrödinger equations on the half line. We present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solutions to equations by using...
作者:Nakao Hayashi , Pavel I. Naumkin
来源:[J].Journal of Differential Equations(IF 1.48), 2015, Vol.258 (3), pp.880-905
摘要:Abstract(#br)We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation in the super critical case i ∂ t u + 1 4 ∂ x 4 u = λ ∂ x ( | u | ρ − 1 u ) , where ρ > 4 , λ ∈ C . We prove the global existence and the large time asymptotics of s...
作者:Nakao Hayashi , Pavel I. Naumkin , Masayo Tominaga
来源:[J].Journal of Mathematical Analysis and Applications(IF 1.05), 2015, Vol.428 (1), pp.490-501
摘要:Abstract(#br)We study global existence of small solutions to the Cauchy problem for a weakly coupled nonlinear damped wave equation { ( ∂ t 2 + ∂ t − Δ ) u = N 1 ( v ) , ( ∂ t 2 + ∂ t − Δ ) v = N 2 ( u ) , x ∈ R n , t > 0 u ( 0 , x ) ...
作者:Nakao Hayashi , Pavel I. Naumkin
来源:[J].Nonlinear Analysis(IF 1.64), 2015, Vol.116, pp.112-131
摘要:Abstract(#br)We consider the Cauchy problem for the nonlinear fourth-order nonlinear Schrödinger equation { i ∂ t u + 1 4 ∂ x 4 u = i λ ∂ x ( | u | 3 u ) , t > 0 , x ∈ R, u ( 0 , x ) = u 0 ( x ) , ...
作者:Nakao Hayashi , Pavel I. Naumkin
来源:[J].Journal of Functional Analysis(IF 1.252), 2016, Vol.270 (6), pp.1971-1994
摘要:Abstract(#br)We study the existence of the wave operators for the nonlinear Klein–Gordon equation with quadratic nonlinearity in two space dimensions ( ∂ t 2 − Δ + 1 ) u = λ u 2 , ( t , x ) ∈ R × R 2 . We prove existence of wave operators in lower order Sobolev spa...
作者:Nakao Hayashi , Chunhua Li , Pavel I. Naumkin
来源:[J].Journal of Differential Equations(IF 1.48), 2016, Vol.260 (2), pp.1472-1495
摘要:Abstract(#br)We consider nonlinear Schrödinger systems with quadratic nonlinearities in two space dimensions. We prove the existence of modified wave operators and uniform time decay of solutions when the Fourier transform of the final data does not necessarily decay at spat...
作者:Nakao Hayashi , Jesus A. Mendez-Navarro , Pavel I. Naumkin
来源:[J].Journal of Differential Equations(IF 1.48), 2016, Vol.261 (9), pp.5144-5179
摘要:Abstract(#br)We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation { i ∂ t u − 1 4 ∂ x 4 u = λ | u | 4 u , ( t , x ) ∈ R + × R , u ( 0 , x ) = u 0 ( x ) , x ∈ R . We prove the large time asymptotic behavior of solutions with a logarithm...
作者:Nakao Hayashi , Pavel I. Naumkin
来源:[J].Communications in Mathematical Physics(IF 1.971), 2015, Vol.335 (2), pp.713-738
摘要:Abstract(#br) We consider the Cauchy problem for the reduced Ostrovsky equation $$u_{tx} = u + \left(u^{3}\right)_{xx}$$ with real valued initial data \({u \left(0\right) = u_{0}}\) . We introduce the factorization for the free evolution group to prove the global existence of sol...

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