共查询到19条相似文献,搜索用时 62 毫秒
1.
拟微分算子理论中,算子象征决定了算子性质.本文在含参数Sobolev空间H;(τ≥τ0>0)的框架下,讨论了相应的含参数象征的拟微分算子的有关性质,并应用微局部分析方法获得该类算子的拟局部性质.从而对经典拟微分算子作了一类推广. 相似文献
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超紧集的刻划与层次结构 总被引:1,自引:0,他引:1
本文给出了LF集的超紧性的网式、滤子式等几种刻划,剖析了超紧集的层次结构,得出了在导出分明拓扑满足T2分离性的前提下子集的超紧性与其任一α-截集的紧性等价等一系列结果。 相似文献
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本文给出一类化学反应的三维数学模型,研究了该模型的波前解的存在性及最小波速。得到了比较完善的结果。 相似文献
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研究了具有非局部时滞的扩散Nicholson苍蝇方程,其中时滞由一个定义在所有过去时间和整个一维空间区域上的积分卷积表示.当时滞核是强生成核时,根据线性链式技巧和几何奇异扰动理论,获得了小时滞时波前解的存在性. 相似文献
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用Level Set算法模拟孤立波与前台阶的相互作用 总被引:1,自引:0,他引:1
进一步研究了Level Set方法的数学基础,研究了求解有自由水面水动力学问题的具体方法。并在此基础上,对孤立波与前台阶相互作用这一问题进行了计算及研究,取得了与实验结果相符合的计算结果。 相似文献
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本文研究了一些拟线性Burgers型方程的波前解的存在性、稳定性,利用谱分析的方法,证明了光滑波前解在某些加权空间中的渐近稳定性。 相似文献
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与一维空间中研究连接两个常数的波前解的存在性不同的是,本文建立了在多维无限长的柱体内连接两个曲面的单调行波解的存在性.相应的模型是一种具有指数率的Logistic方程.所用的方法是一种改进了的单调性方法.本文的研究结果对自然界中波的实际传播行为给出了有益的启示. 相似文献
11.
Hua Chen 《数学学报(英文版)》2001,17(2):295-300
In this note, we use the so-called microlocal energy method to give a characterization of the Gevrey-Sobolev wave front set
, which will be useful in the study of non-linear microlocal analysis in Gevrey classes.
Research supported by grants of the Natural Science Foundation of China, the State Education Committee and
the Huacheng Foundation. 相似文献
12.
We discuss the mathematical aspects of wave field measurements used in traveltime inversion from seismograms. The primary information about the medium is assumed to be carried by the wave front set and its perturbation with respect to a hypothetical background medium is to be estimated. By a convincing heuristics a detection procedure for this perturbation was proposed based on optimization of wave field correlations. We investigate its theoretical foundation in simple mathematical case studies using the distribution theoretic definition of oscillatory integrals. 相似文献
13.
Wave front set for solutions to Schrödinger equations with long-range perturbed harmonic oscillators
In this paper we consider a Schrödinger operator with variable coefficients and harmonic potential. The perturbation is assumed to be long-range in a sense similar to the work of Nakamura (2009) [13]. We construct a modified propagator, and then by using this propagator and also the propagator of the unperturbed free harmonic oscillator we characterize the propagation of singularities for solutions to the equations. 相似文献
14.
We discuss a notion of wave front set which allows us tocontrol the behaviour `at infinity' of temperate distributions. Weobtain the microlocality and microellipticity properties with respect toa class of global pseudodifferential operators and a propagation theoremfor the corresponding class of Fourier Integral Operators. Through theseresults, we prove an adapted global version of the classical theoremconcerning the singularities of solutions of hyperbolic Cauchy problemsfor linear operators with multiple characteristics of constantmultiplicities. Finally, we make a comparison with the scattering wavefront set introduced by Melrose. 相似文献
15.
In this paper by using upper-lower solution method, under appropriate assumptions on f and g the existence of travelling wave front solutions for the following reaction-diffusion system is proved: {u_t - u_{xx}, = f(u,v) v_t - v_{xx} = g(u, v) As an application, the necessary and sufficient condition of the existence of monotone solutions for the boundary value problem {u" + cu' + u(1 - u- rv) = 0 v" + cv' - buv = 0 u(-∞) = v(+∞) = 0 u(+∞) = v(-∞) = 1 where 0 < r < 1, 0 < b < \frac{1 - r}{r} are known constants and c is unknown constant to be obtained. 相似文献
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Shu Nakamura 《Journal of Functional Analysis》2009,256(4):1299-1309
We consider solutions to Schrödinger equation on Rd with variable coefficients. Let H be the Schrödinger operator and let u(t)=e−itHu0 be the solution to the Schrödinger equation with the initial condition u0∈L2(Rd). We show that the wave front set of u(t) in the nontrapping region can be characterized by the wave front set of e−itH0u0, where H0 is the free Schrödinger operator. The characterization of the wave front set is given by the wave operator for the corresponding classical mechanical scattering (or equivalently, by the asymptotics of the geodesic flow). 相似文献
17.
Li Zhengyuan 《偏微分方程(英文版)》1992,5(1)
In this paper by using upper-lower solution method the critical wave speed of wave front for a simplified mathematical model of Belousov-Zhabotinskii chemical reaction u_t - u_{xx} = u(1 - u - rv) v_t - v_{xx} = -buv is obtained, where 0 < r < 1, b > 0 are known. 相似文献
18.
Claude-Michel BRAUNER Luca LORENZI Gregory I. SIVASHINSKY Chuanju XU 《数学年刊B辑(英文版)》2010,31(6):819-840
In two-dimensional free-interface problems, the front dynamics can be modeled by single parabolic equations such as the Kuramoto-Sivashinsky equation (K-S). However, away from the stability threshold, the structure of the front equation may be more involved. In this paper, a generalized K-S equation, a nonlinear wave equation with a strong damping operator, is considered. As a consequence, the associated semigroup turns out to be analytic. Asymptotic convergence to K-S is shown, while numerical results illustrate the dynamics. 相似文献
19.
Dean Baskin 《Journal of Functional Analysis》2010,259(7):1673-1719
In this paper we construct a parametrix for the forward fundamental solution of the wave and Klein-Gordon equations on asymptotically de Sitter spaces without caustics. We use this parametrix to obtain asymptotic expansions for solutions of (□−λ)u=f and to obtain a uniform Lp estimate for a family of bump functions traveling to infinity. 相似文献