共查询到20条相似文献,搜索用时 0 毫秒
1.
Maria Psarelli 《偏微分方程通讯》2013,38(1-2):273-282
Abstract. In this paper I derive a gauge invariant decay estimate of the solutions of massive Maxwell—Klein—Gordon fields equations in the 4—dimensional Minkowski space, provided that the initial energy of the system is bounded. This estimate implies that the Klein—Gordon field decays to zero in the local L2 norm. I also show that the local energy decays. The proof is based on gauge invariant energy identities. 相似文献
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Nikolaos Bournaveas 《偏微分方程通讯》2013,38(7-8):1167-1193
Abstract We show a method to eliminate a type of mixed asymptotics in certain free boundary problems, and give two examples of its application. It appears that these problems cannot be handled by the monotonicity formula of Alt et al. [Alt, H. W., Caffarelli, L. A., Friedman, A. (1984). Variational problems with two phases and their free boundaries. Trans. Am. Math. Soc. 282(2):431–461] or by the more recent monotonicity formula of Caffarelli et al. [Caffarelli, L. A., Jerison, D., Kenig, C. E. (2002). Some new monotonicity theorems with applications to free boundary problems. Ann. Math. (2) 155(2):369–404]. 相似文献
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Asymptotic behavior of the solutions of the p-Laplacian equation 总被引:1,自引:0,他引:1
ZHANG Liqin & ZHAO Junning Department of Mathematics Xiamen University Xiamen China 《中国科学A辑(英文版)》2006,49(6)
The asymptotic behavior of the solutions for p-Laplacian equations as p→∞ is studied. 相似文献
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In this paper, we will analyze further to obtain a finer asymptotic behavior of positive solutions of semilinear elliptic equations in R^n by employing the Li's method of energy function. 相似文献
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M. D. Surnachev 《Journal of Mathematical Sciences》2011,177(1):148-207
We study the asymptotic behavior of positive solutions to nonlinear elliptic equations of Emden–Fowler type with absorption
term. For operators with variable coefficients we obtain conditions on coefficients under which the solutions have the same
asymptotics as solutions to the model equation Δu = −x|
p
|u|
σ−1
u. For positive solutions we obtain lower order terms of the asymptotic expansion at infinity. Bibliography: 10 titles. 相似文献
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Theoretical and Mathematical Physics - We consider the modernized Camassa—Holm equation with periodic boundary conditions. The quadratic nonlinearities in this equation differ substantially... 相似文献
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We study the large time behavior of solutions of the Cauchy problem for the Hamilton–Jacobi equation ut+H(x,Du)=0 in Rn×(0,∞), where H(x,p) is continuous on Rn×Rn and convex in p . We establish a general convergence result for viscosity solutions u(x,t) of the Cauchy problem as t→∞. 相似文献
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A. P. Oskolkov 《Journal of Mathematical Sciences》1991,56(2):2396-2402
It is shown that for the nonstationary equations of motion of the linear viscoelastic fluids, whose defining equation has the form the stationary system is the Navier-Stokes stationary system with viscosity coefficient v: It is proved that for small Reynolds numbers the solutions of the initial-boundary value problems for the equations of motion of the Oldroyd fluids (M=L=1, 2, ...) and Kelvin-Voight fluids (M=L + 1, L=0, 1, 2, ...) converge for t to the solution of the first boundary value problem for the stationary Navier-Stokes system (*).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 171, pp. 174–181, 1989. 相似文献
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Mehdi Belraouti 《Geometriae Dedicata》2017,186(1):103-112
We present some new examples of families of cubic hypersurfaces in \(\mathbb {P}^5 (\mathbb {C})\) containing a plane whose associated quadric bundle does not have a rational section. 相似文献
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Donatella Donatelli Ming Mei Bruno Rubino Rosella Sampalmieri 《Journal of Differential Equations》2013
In this paper we study the Cauchy problem for 1-D Euler–Poisson system, which represents a physically relevant hydrodynamic model but also a challenging case for a bipolar semiconductor device by considering two different pressure functions and a non-flat doping profile. Different from the previous studies (Gasser et al., 2003 [7], Huang et al., 2011 [12], Huang et al., 2012 [13]) for the case with two identical pressure functions and zero doping profile, we realize that the asymptotic profiles of this more physical model are their corresponding stationary waves (steady-state solutions) rather than the diffusion waves. Furthermore, we prove that, when the flow is fully subsonic, by means of a technical energy method with some new development, the smooth solutions of the system are unique, exist globally and time-algebraically converge to the corresponding stationary solutions. The optimal algebraic convergence rates are obtained. 相似文献
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In this paper, we study a nematic liquid crystals system in three-dimensional whole space ?3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L1?3 additionally. 相似文献
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In this paper, we first consider difference equations with several delays in the neutral term of the form * $$\Delta\left(y_{n}+\sum_{i=1}^{L}p_{i}y_{n-{k_{i}}}-\sum_{j=1}^{M}r_{j}y_{n-{\rho_{j}}}\right)+q_{n}y_{n-\tau}=0\quad \mbox{for}\ n\in\mathbb{Z}^{+}(0),$$ study various cases of coefficients in the neutral term and obtain the asymptotic behavior for non-oscillatory solution of (*) under some hypotheses. Moreover, we consider reaction-diffusion difference equations with several delays in the neutral term of the form $$\begin{array}{l}\Delta_{1}\left(u_{n,m}+\displaystyle \sum_{i=1}^{L}p_{i}u_{n-{k_{i}},m}-\displaystyle \sum_{j=1}^{M}r_{j}u_{n-{\rho_{j}},m}\right)+q_{n,m}u_{n-\tau,m}\\[18pt]\quad {}=a^{2}\Delta_{2}^{2}u_{n+1,m-1}\end{array}$$ for (n,m)∈?+(0)×Ω, study various cases of coefficients in the neutral term and obtain the asymptotic behavior for non-oscillatory solution under some hypotheses. 相似文献
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G. T. Kossioris 《偏微分方程通讯》2013,38(5-6):747-770
In this work we study the generation and propagation of singularities (shock waves) of the solution of the Cauchy problem for Hamilton-Jacobi equations in one space variable, under no assumption on the convexity or concavity of the hamiltonian. We study the problem in the class of viscosity solutions, which is the correct class of weak solutions. We obtain the exact global structure of the shock waves by studying the way the characteristics cross. We construct the viscosity solution by either selecting a single-valued branch of the multi-valued function given as a solution by the method of characteristics or constructing explicitly the proper rarefaction waves. 相似文献
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The large time behavior of zero-mass solutions to the Cauchy problem for the convection–diffusion equation is studied when q>1 and the initial datum u0 belongs to and satisfies . We provide conditions on the size and shape of the initial datum u0 as well as on the exponent q>1 such that the large time asymptotics of solutions is given either by the derivative of the Gauss–Weierstrass kernel, or by a self-similar solution of the equation, or by hyperbolic N-waves. To cite this article: S. Benachour et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献