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1.
Kenji Nishihara 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(4):604-614
We consider the Cauchy problem for the nonlinear dissipative evolution system with ellipticity on one dimensional space
with
S. Q. Tang and H. Zhao [4] have considered the problem and obtained the optimal decay property for suitably small data. In
this paper we derive the asymptotic profile using the Gauss kernel G(t, x), which shows the precise behavior of solution as time tends to infinity. In fact, we will show that the asymptotic formula
holds, where D0, β0 are determined by the data. It is the key point to reformulate the system to the nonlinear parabolic one by suitable changing
variables.
(Received: January 8, 2005) 相似文献
2.
Changjiang Zhu Zhian Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(6):994-1014
In this paper, we study the global existence and the asymptotic behavior of the solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects
with initial data
where and are positive constants such that < 1, < (1–). Through constructing a correct function
defined by (2.13) and using the energy method, we show
as
and the solutions decay with exponential rates. The same problem is studied by Tang and Zhao [10] for the case of (±, ±) = (0,0).Received: November 18, 2003 相似文献
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3.
Zhian Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,22(5):399-418
We derive the optimal decay rates of solution to the Cauchy problem for a set of nonlinear evolution equations with ellipticity
and dissipative effects
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$\left\{ \begin{aligned} & \psi t = - (1 - \alpha )\psi - \theta _{x} + \alpha \psi _{{xx}} , \\ & \theta _{t} = - (1 - \beta )\theta + \nu \psi _{x} + 2\psi \theta _{x} + \alpha \theta _{{xx}} , \\ \end{aligned} \right.$\left\{ \begin{aligned} & \psi t = - (1 - \alpha )\psi - \theta _{x} + \alpha \psi _{{xx}} , \\ & \theta _{t} = - (1 - \beta )\theta + \nu \psi _{x} + 2\psi \theta _{x} + \alpha \theta _{{xx}} , \\ \end{aligned} \right. 相似文献
4.
Zhian Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(3):399-418
We derive the optimal decay rates of solution to the Cauchy problem for a set of nonlinear evolution equations with ellipticity
and dissipative effects
5.
We investigate the asymptotic profile to the Cauchy problem for a non‐linear dissipative evolution system with conservational form (1) provided that the initial data are small, where constants α, ν are positive satisfying ν2<4α(1 ? α), α<1. In (J. Phys. A 2005; 38 :10955–10969), the global existence and optimal decay rates of the solution to this problem have been obtained. The aim of this paper is to apply the heat kernel to examine more precise behaviour of the solution by finding out the asymptotic profile. Precisely speaking, we show that, when time t → ∞ the solution and solution in the Lp sense, where G(t, x) denotes the heat kernel and is determined by the initial data and the solution to a reformulated problem obtained in Section 3, β is related to ?+ and ?? which are determined by (41) in Section 4. The numerical simulation is presented in the end. The motivation of this work thanks to Nishihara (Asymptotic profile of solutions to nonlinear dissipative evolution system with ellipticity. Z. Angew Math Phys 2006; 57 : 604–614). Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
6.
We establish the global existence and decaying results for the Cauchy problem of nonlinear evolution equations:
(E) 相似文献
7.
Renjun Duan 《Journal of Mathematical Analysis and Applications》2005,303(1):15-35
In this paper, we consider the global existence and asymptotic behaviors of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects:
(E) 相似文献
8.
This paper is concerned with the asymptotic behavior of the two-dimensional dissipative quasi-geostrophic equation. Based on the spectral decomposition of the Laplacian operator and iterative techniques, we obtain improved L 2 decay rates of weak solutions and derive more explicit upper bounds of higher order derivatives of solutions. We also prove the asymptotic stability of the subcritical quasi-geostrophic equation under large initial and external perturbations. 相似文献
9.
Hu Wei 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):5897-5905
In this paper, we consider the local existence of solutions to the Cauchy problems for the following nonlinear evolution equations with mixed types
10.
11.
In this paper, we consider an initial boundary value problem for some nonlinear evolution system with dissipation and ellipticity. We establish the global existence and furthermore obtain the Lp (p?2) decay rates of solutions corresponding to diffusion waves. The analysis is based on the energy method and pointwise estimates. 相似文献
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14.
Marianna Ruggieri Maria Paola Speciale 《Mathematical Methods in the Applied Sciences》2020,43(13):7569-7578
In this paper, the problem of approximate symmetries of a class of nonlinear wave equations with a small nonlinear dissipation has been investigated. In order to compute the first-order approximate symmetry, we have applied the method that was proposed by Valenti basically based on the expansion of the dependent variables in perturbation series but removing the drawback of the impossibility to work in hierarchy in calculating symmetries. The algebraic structure of the approximate symmetries is discussed, an optimal system of one-dimensional subalgebras is defined and constructed, and, finally, some invariant solutions corresponding to the resulted symmetries are obtained. 相似文献
15.
Zhian Wang 《Journal of Mathematical Analysis and Applications》2006,319(2):740-763
We derive the optimal convergence rates to diffusion wave for the Cauchy problem of a set of nonlinear evolution equations with ellipticity and dissipative effects
16.
Asymptotic profile of solutions for the damped wave equation with a nonlinear convection term
 下载免费PDF全文 This paper is concerned with the large time behavior of solutions to the initial value problem for the damped wave equations with nonlinear convection in one‐dimensional whole space. In 2007, Ueda and Kawashima showed that the solution tends to a self similar solution of the Burgers equation. However, they did not mention that their decay estimate is optimal or not. Under this situation, the aim of this paper was to find out the sharp decay estimate by studying the second asymptotic profile of solutions. The explicit representation formula and the decay estimates of the solution for the linearized equation including the lower order term play crucial roles in our analysis. 相似文献
17.
In this paper, the asymptotic behavior of the solution to the initial–boundary value problem for a nonlinear evolution equation of fourth order
equation(1) utt−a1uxx−a2uxxt−a3uxxtt=φ(ux)x 18.
Walter Allegretto 《Journal of Mathematical Analysis and Applications》2008,347(1):344-353
In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects
(E) 相似文献
19.
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