Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation

Kawashima, Shuichi; Wang, Yu Zhu

doi:10.1142/s021953051450002x

Cited by 24 publications

(27 citation statements)

References 29 publications

(28 reference statements)

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“…We may refer to [6,8,[16][17][18][21][22][23][24]. For quantum stochastic evolution inclusions and variational inclusions, some related results have been established in [12].…”

Section: Equation (14) Has the Following Generalized Formmentioning

confidence: 99%

On properties of solutions to the improved modified Boussinesq equation

Wang¹,

Wang²

2016

J. Nonlinear Sci. Appl.

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In this paper, we investigate the Cauchy problem for the generalized IBq equation with damping in one dimensional space. When σ = 1, the nonlinear approximation of the global solutions is established under small condition on the initial value. Moreover, we show that as time tends to infinity, the solution is asymptotic to the superposition of nonlinear diffusion waves which are given explicitly in terms of the selfsimilar solution of the viscous Burgers equation. When σ ≥ 2, we prove that our global solution converges to the superposition of diffusion waves which are given explicitly in terms of the solution of linear parabolic equation. c 2016 all rights reserved.

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“…We may refer to [6,8,[16][17][18][21][22][23][24]. For quantum stochastic evolution inclusions and variational inclusions, some related results have been established in [12].…”

Section: Equation (14) Has the Following Generalized Formmentioning

confidence: 99%

On properties of solutions to the improved modified Boussinesq equation

Wang¹,

Wang²

2016

J. Nonlinear Sci. Appl.

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“…The estimate (2.15) may be derived by applying the energy method in the Fourier space to (2.12). Such an energy method was first developed in [20] and then used in many papers (see, for example, [11,12,23,25]). Here, for the convenience to the readers, we give the complete proof.…”

Section: Decay Propertiesmentioning

confidence: 99%

Asymptotic behavior of classical solutions to the compressible Navier–Stokes–Poisson equations in three and higher dimensions

Wang

2015

Journal of Differential Equations

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In this paper, we consider the initial value problem for the compressible Navier-Stokes-Poisson equations in three and higher dimensions. Firstly, global existence and new decay estimate of classical solutions are established. The proof is mainly based on the decay properties of solution operator to the compressible Navier-Stokes-Poisson equations, which may be derived from the pointwise estimate of the solution operator to a linear wave equation that is corresponding to the density function, while the pointwise estimate of solution operator to the linear wave equation may be established by an energy method in the Fourier space. The method is different from those in previous works on decay estimate of solutions to compressible Navier-Stokes-Poisson equations. Finally, asymptotic profile of the solution to the corresponding linear problem is also investigated.

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“…The estimate (2.16) may be derived by applying the energy method in the Fourier space to (2.13). Such an energy method was first developed in [21] and then used in many papers (see, for example, [14,12,[23][24][25]). Here, for the convenience to the readers, we give the complete proof.…”

Section: Decay Propertiesmentioning

confidence: 99%

Long time behavior of solutions to the compressible MHD system in multi-dimensions

Wang

2015

Journal of Mathematical Analysis and Applications

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In this paper, we consider the initial value problem for the compressible MHD system in multi-dimensions. Under suitable conditions on the initial value, the global existence and long time behavior of classical solutions are established. Moreover, we also show that the solution can be approximated by the linear solution as time tends to infinity. The proof is based on the decay properties of solution operator to the compressible MHD system, which may be given in terms of the heat kernel and the solution operator to a linear wave equation that is corresponding to the density function. The decay properties of solution operators to the compressible MHD system may be derived from the pointwise estimate of solution operator to the linear wave equation. Finally, asymptotic profile to the linear system is also established.

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Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation

Cited by 24 publications

References 29 publications

On properties of solutions to the improved modified Boussinesq equation

On properties of solutions to the improved modified Boussinesq equation

Asymptotic behavior of classical solutions to the compressible Navier–Stokes–Poisson equations in three and higher dimensions

Long time behavior of solutions to the compressible MHD system in multi-dimensions

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