Initial–boundary value problem of Euler equations with damping in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:msubsup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:math>

Du, Li

doi:10.1016/j.na.2018.06.014

Cited by 5 publications

(6 citation statements)

References 21 publications

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“…However, it is quite difficult to inverse the master relationship especially for the system in high dimensional case. Series of applications and improvements of this method were given by [3,5,6,8,10,20,29] and the reference therein. They improved the procedure to simplify the complicated computations of inverse Fourier and Laplace transforms with the help of a deep understanding of the connections of the different symbols.…”

Section: Linglong Dumentioning

confidence: 99%

“…However, for the high dimensional case the boundary surface operator could be very complicated for system of equations, see [5,20,29]. In paper [10], by comparing symbols in the transformed tangential-spatial and time space, the author showed that one can simplify the Green's function for the half space problem to essential part. In this paper, we use the same approach to get the simplified expression of the Green's functions, and they benefit the follow-up nonlinear analysis.…”

Section: Linglong Dumentioning

confidence: 99%

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Long time behavior for the visco-elastic damped wave equation in <inline-formula><tex-math id="M1">\begin{document}$\mathbb{R}^n_+$\end{document}</tex-math></inline-formula> and the boundary effect

Du¹

2018

Networks &Amp; Heterogeneous Media

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In this paper, we investigate the existence and long time behavior of the solution for the nonlinear visco-elastic damped wave equation in R n + , provided that the initial data is sufficiently small. It is shown that for the long time, one can use the convected heat kernel to describe the hyperbolic wave transport structure and damped diffusive mechanism. The Green's function for the linear initial boundary value problem can be described in terms of the fundamental solution (for the full space problem) and reflected fundamental solution coupled with the boundary operator. Using the Duhamel's principle, we get the L p decaying rate for the nonlinear solution ∂ α x u for |α| ≤ 1.

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Section: Linglong Dumentioning

confidence: 99%

Section: Linglong Dumentioning

confidence: 99%

Long time behavior for the visco-elastic damped wave equation in <inline-formula><tex-math id="M1">\begin{document}$\mathbb{R}^n_+$\end{document}</tex-math></inline-formula> and the boundary effect

Du¹

2018

Networks &Amp; Heterogeneous Media

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“…Kawashima [11,10] obtained the L 2 time decay rate of several general hyperbolic-parabolic systems with applications to related models. The optimal L 2 time decay rate for the threedimensional full N-S system was investigated by Mastumura and Nishida [22] when the initial data is a small perturbation of constant state in H 3…”

mentioning

confidence: 99%

Pointwise estimates of the solution to one dimensional compressible Naiver-Stokes equations in half space

Li¹,

Tang²,

Wang³

2022

DCDS

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<p style='text-indent:20px;'>In this paper, we study the global existence and pointwise behavior of classical solution to one dimensional isentropic Navier-Stokes equations with mixed type boundary condition in half space. Based on classical energy method for half space problem, the global existence of classical solution is established firstly. Through analyzing the quantitative relationships of Green's function between Cauchy problem and initial boundary value problem, we observe that the leading part of Green's function for the initial boundary value problem is composed of three items: delta function, diffusive heat kernel, and reflected term from the boundary. Then applying Duhamel's principle yields the explicit expression of solution. With the help of accurate estimates for nonlinear wave coupling and the elliptic structure of velocity, the pointwise behavior of the solution is obtained under some appropriate assumptions on the initial data. Our results prove that the solution converges to the equilibrium state at the optimal decay rate <inline-formula><tex-math id="M1">\begin{document}$ (1+t)^{-\frac{1}{2}} $\end{document}</tex-math></inline-formula> in <inline-formula><tex-math id="M2">\begin{document}$ L^\infty $\end{document}</tex-math></inline-formula> norm.</p>

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“…The way of estimating the Green's functions G i was initiated by [17] and developed by [3,5,6,8,10,18,24] and the reference therein. Following the scheme in [10], we will find the relations between the fundamental solutions for the linear Cauchy problem and Green's functions for the linear half space problem, by comparing their symbols in the transformed tangential-spatial and time variables. Then the Green's functions can be described in terms of the fundamental solutions and the boundary surface operator.…”

mentioning

confidence: 99%

“…Lemma 5.1. [10] In the finite Mach number region |x| ≤ 4(t + 1), we have the following estimate for the inverse Fourier transform:…”

mentioning

confidence: 99%

Pointwise long time behavior for the mixed damped nonlinear wave equation in

Yang

2021

NHM

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Initial–boundary value problem of Euler equations with damping in R+n

Cited by 5 publications

References 21 publications

Long time behavior for the visco-elastic damped wave equation in <inline-formula><tex-math id="M1">\begin{document}$\mathbb{R}^n_+$\end{document}</tex-math></inline-formula> and the boundary effect

Long time behavior for the visco-elastic damped wave equation in <inline-formula><tex-math id="M1">\begin{document}$\mathbb{R}^n_+$\end{document}</tex-math></inline-formula> and the boundary effect

Pointwise estimates of the solution to one dimensional compressible Naiver-Stokes equations in half space

Pointwise long time behavior for the mixed damped nonlinear wave equation in

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