Asymptotics of solutions to the periodic problem for the nonlinear damped wave equation

Hayashi, Nakao; Naumkin, Pavel I.; Rodriguez-Ceballos, Joel A.

doi:10.1007/s00030-010-0058-1

Cited by 4 publications

(1 citation statement)

References 33 publications

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“…For the Benjamin-Bona-Mahony-Peregrine-Burgers equation, the existence of global solutions and decay estimates of energy were obtained in paper [26]. Asymptotics of solutions to the periodic problem for the nonlinear damped wave equation was studied in paper [14]. Large time behavior of solutions to the periodic problem for systems of conservation laws was studied in [8,24].…”

Section: Introductionmentioning

confidence: 99%

Asymptotics of solutions to the periodic problem for a Burgers type equation

Naumkin

Rojas-Milla

2010

J. Evol. Equ.

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We study large time asymptotic behavior of solutions to the periodic problem for the nonlinear Burgers type equationwhere = [−π, π], λ < 1. We prove that if the initial data ψ ∈ L 2 ( ), then there exists a unique solution ψ(t, x) ∈ C [0, ∞); L 2 ( ) ∩ C ∞ ((0, ∞) × R) of the periodic problem. Moreover, under some additional conditions we find the asymptotic expansion for the solutions.

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Section: Introductionmentioning

confidence: 99%

Asymptotics of solutions to the periodic problem for a Burgers type equation

Naumkin

Rojas-Milla

2010

J. Evol. Equ.

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Large time asymptotics of solutions to the periodic problem for the quadratic nonlinear Schrödinger equation

Hayashi

Naumkin

2022

Nonlinear Differ. Equ. Appl.

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Asymptotics of Solutions for Periodic Problem for the Korteweg-de Vries Equation with Landau Damping, Pumping and Higher Order Convective Non Linearity

Juárez-Campos,

Villela-Aguilar,

Carreño-Bolaños

2023

J Nonlinear Math Phys

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We study the periodic problem for the Korteweg–de Vries equation with Landau damping, linear pumping and a higher-order convective nonlinearity $$\begin{aligned} \left\{ \begin{array}{c} w_{t}+w_{xxx}-\alpha w_{xx}=\beta w+\lambda w_{x}^{2}w_{xx},\text { }x\in \Omega ,t>0,\\ w(0,x)=\psi \left( x\right) ,\text { }x\in \Omega , \end{array} \right. \end{aligned}$$ w t + w xxx - α w xx = β w + λ w x 2 w xx , x ∈ Ω , t > 0 , w ( 0 , x ) = ψ x , x ∈ Ω , where, $$\alpha ,\beta >0,$$ α , β > 0 , $$\lambda \in \mathbb {R},$$ λ ∈ R , $$\Omega =\left[ -\pi ,\pi \right] .$$ Ω = - π , π . We assume that the initial data $$\psi \left( x\right) $$ ψ x are $$2\pi $$ 2 π - periodic. We prove the global existence of solutions and analyze their large-time asymptotics.

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Asymptotics of solutions to the periodic problem for the nonlinear damped wave equation

Cited by 4 publications

References 33 publications

Asymptotics of solutions to the periodic problem for a Burgers type equation

Asymptotics of solutions to the periodic problem for a Burgers type equation

Large time asymptotics of solutions to the periodic problem for the quadratic nonlinear Schrödinger equation

Asymptotics of Solutions for Periodic Problem for the Korteweg-de Vries Equation with Landau Damping, Pumping and Higher Order Convective Non Linearity

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