具有阻尼的半线性波动方程解的衰减估计

研究具有阻尼的半线性波动方程的初边值问题u_(tt)-△u+βu_t=|u|~(p-1)u,x∈Ω,t>0u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈Ωu|_((?)Ω)=0,t≥0其中γ为正常数,Ω■R~n为有界域,当n≥3时,1相似文献   

SOLVABILITY FOR FRACTIONAL-ORDER TWO-POINT BOUNDARY VALUE PROBLEM AT RESONANCE

In this paper, we are concerned with the existence of solution to a boundary value problem of nonlinear fractional differential equation at resonance. By means of the coincidence degree theory, the existence of solution is obtained.     

正则长波方程的三次配点法

本文讨论了正则长波方程(RLW方程)的三次配点法,得到半离散格式的最优阶误差估计,同时给出基于向后Euler法的全离散格式,并证明了相应的误差估计.     

On the Hughes' model for pedestrian flow: The one-dimensional case

In this paper we investigate the mathematical theory of Hughes' model for the flow of pedestrians (cf. Hughes (2002) [17]), consisting of a non-linear conservation law for the density of pedestrians coupled with an eikonal equation for a potential modelling the common sense of the task. For such an approximated system we prove existence and uniqueness of entropy solutions (in one space dimension) in the sense of Kru?kov (1970) [22], in which the boundary conditions are posed following the approach of Bardos et al. (1979) [7]. We use BV estimates on the density ρ and stability estimates on the potential ? in order to prove uniqueness. Furthermore, we analyze the evolution of characteristics for the original Hughes' model in one space dimension and study the behavior of simple solutions, in order to reproduce interesting phenomena related to the formation of shocks and rarefaction waves. The characteristic calculus is supported by numerical simulations.     

Partial regularity of finite Morse index solutions to the Lane-Emden equation

We prove regularity and partial regularity results for finite Morse index solutions u∈H¹(Ω)∩Lp(Ω) to the Lane-Emden equation −Δu=|u|^p−1u in Ω.     

New generalized Jacobi elliptic function rational expansion method

In this work, a new generalized Jacobi elliptic function rational expansion method is based upon twenty-four Jacobi elliptic functions and eight double periodic Weierstrass elliptic functions, which solve the elliptic equation ?^′2=r+p?²+q?⁴, is described. As a consequence abundant new Jacobi-Weierstrass double periodic elliptic functions solutions for (3+1)-dimensional Kadmtsev-Petviashvili (KP) equation are obtained by using this method. We show that the new method can be also used to solve other nonlinear partial differential equations (NPDEs) in mathematical physics.     

新的适用于整个热力面的1,1,1,2-四氟乙烷(R134a)跨接状态方程

1前言作者建立了一个新型的符合临界重整化群理论的跨接状态方程，能够描述物质的整个区域热力性质山。鉴于R134a是R12的新的主要替代制冷剂，为了计算其整个区域的热力性质，本文将新跨接状态方程应用于R134a，以便提供一个能在整个区域计算R134a热力性质的状态方程。2新跨接状态方程作者建立了以下型式的新跨接状态方程l‘］：上式中，西方一r一IDZ户一p巾c；，一DI—TD；T—To／T；产为密度；pc为临界密度；T为温度；To为临界温度；矿对比过余Helmholtz自由能；A是Helmholtz自由能。新函数中，a。一30，a，一10；0—0．325和西一…     

丢翻图方x2 + a2=2yn解法的计算研究

本文研究了一类丢番图方程的解.利用对Thue方程解的估计和方程解的连分式展开,获得了所求丢番图方程解的个数、解上界的估计和一般的求解算法.最后利用该算法给出了1≤a≤108的所有解.     

半线性Sobolev方程的H~1-Galerkin混合有限元方法

利用H~1-Galerkin混合有限元方法研究了一维半线性Sobolev方程,得到了半离散解的最优阶误差估计,优点是不需验证LBB相容性条件.