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24 results on '"GENG, SHIFENG"'

2. The time asymptotic expansion for the compressible Euler equations with time-dependent damping

Author

Geng, Shifeng, Huang, Feimin, Jin, Guanghui, and Wu, Xiaochun

Subjects
Mathematics - Analysis of PDEs
Abstract

In this paper, we study the compressible Euler equations with time-dependent damping $-\frac{1}{(1+t)^{\lambda}}\rho u$. We propose a time asymptotic expansion around the self-similar solution of the generalized porous media equation (GPME) and rigorously justify this expansion as $\lambda \in (\frac17,1)$. In other word, instead of the self-similar solution of GPME, the expansion is the best asymptotic profile of the solution to the compressible Euler equations with time-dependent damping.

Published
2022
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22. L-convergence rates to nonlinear diffusion waves for quasilinear equations with nonlinear damping.

Author

Geng, Shifeng and Zhang, Lina

Subjects
STOCHASTIC convergence, QUASILINEARIZATION, BURGERS' equation, DAMPING (Mechanics), HYPERBOLIC differential equations
Abstract

This paper is concerned with the asymptotic behavior of the solution for quasilinear hyperbolic equations with nonlinear damping. The main novelty in this paper is that we obtain the L(2 ≤ p ≤ +∞) convergence rates of the solution to the quasilinear hyperbolic equations, and we need none of the additional technical assumptions for the nonlinear damping f( v) given by Li and Saxton (Q Appl Math 61:295-313, ). [ABSTRACT FROM AUTHOR]

Published
2015
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23. convergence rates of solutions for n-dimensional quasilinear damped wave equation.

Author

Geng, Shifeng and Wang, Zhen

Subjects
*STOCHASTIC convergence, *DIMENSIONAL analysis, *QUASILINEARIZATION, *DAMPING (Mechanics), *NUMERICAL solutions to wave equations, *LINEAR equations
Abstract

Abstract: We realize the asymptotic profile for the solutions to the n-dimensional quasilinear damped wave equation in the divergence form is the solution of the corresponding linear parabolic equation with special initial data, and we further show the (in particular, ) convergence rates to this linear asymptotic profile. [Copyright &y& Elsevier]

Published
2014
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24. Convergence Rates to Nonlinear Diffusion Waves for Solutions to the System of Compressible Adiabatic Flow through Porous Media.

Author

Geng, Shifeng and Wang, Zhen

Subjects
*STOCHASTIC convergence, *BURGERS' equation, *COMPRESSIBILITY, *POROUS materials, *ASYMPTOTIC expansions, *NUMERICAL solutions to the Cauchy problem
Abstract

We realize the best asymptotic profile for the solutions to the Cauchy problem of the nonisentropic p-system with damping is a particular solution to the corresponding nonlinear parabolic equation with special initial data, and we further show the convergence rates to this particular asymptotic profile. This new rates are much better than that obtained by Nishihara and Nishikawa [15]. [ABSTRACT FROM AUTHOR]

Published
2011
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