共查询到19条相似文献,搜索用时 46 毫秒
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本文介绍了一种新的几何流, 得到了这种流的一些精确解. 首先得到了初始度量为Einstein的解. 其次得到了具有轴对称的解. 最后,
作为这种流的特殊解, 定义了稳定耗散双曲Yamabe孤子, 而且给出了这种孤子解所满足的方程. 相似文献
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基于Einstein方程和Hamilton Ricci流为背景,孔德兴和刘克峰最近提出了耗散双曲几何流的概念.考虑耗散双曲几何流Cauchy问题,证明了对于任意给定的初始度量,总存在初始的对称张量,使得经典解整体存在,并且对应的曲率保持一致有界.否则,其经典解会在有限时间内破裂. 相似文献
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通过引入恰当的试探函数,将非线性热传导方程化为易于求解的常微分方程组并对其求解,进而得到非线性热传导方程的孤波解、奇异行波解、三角函数周期波解等一些不同形式的行波解. 相似文献
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赵露 《纯粹数学与应用数学》2018,(2):118-127
根据简化的Hirota双线性方法和cole-hopf变换,当双模Jordan KdV方程中的非线性参数与线性参数取特殊值时,得到了双模Jordan KdV方程的多孤子解.同时,当方程中非线性参数与线性参数取一般值,也得到了这个方程的其它的精确解. 相似文献
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罗少盈 《高校应用数学学报(A辑)》2015,(2):217-222
利用特征线方法研究了黎曼流形上的一类新的流-双曲梯度流.给出了光滑解整体存在的充分条件和必要条件.同时获得了解的唯一性和衰减估计. 相似文献
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广义组合KdV-mKdV方程的显式精确解 总被引:1,自引:0,他引:1
Abstract. With the aid of Mathematica and Wu-elimination method,via using a new generalizedansatz and well-known Riccati equation,thirty-two families of explicit and exact solutions forthe generalized combined KdV and mKdV equation are obtained,which contain new solitarywave solutions and periodic wave solutions. This approach can also be applied to other nonlinearevolution equations. 相似文献
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该文研究了N维单位球面SN上的Yamabe方程■通过分歧的方法,对于任意k≥1,证明了该方程对于任意的λ>λk:=(k+N-1)(N-2)/4都至少有一个非常数解vk,使得vk-λ(1/(N*-1))正好有k个零点,并且它们在(-1,1)中都是单根,其中N*是Sobolev临界指数.在应用部分,得到了当n≥4时,RN上非线性椭圆方程非径向解的存在性.此外,还得到了乘积流形中一个流形是单位球时的Yamabe问题的全局分歧结果. 相似文献
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本文得到Yamabe流下拉普拉斯算子的第一特征值的发展方程.我们证明出,在光滑的齐性流形(M(t),g)上,若λ(t)表示拉普拉斯算子的特征值,那么沿着规范化后的Yamabe 流,λ(t)=d,而且沿着非规范化的Yambe流,λ(t)=ded,这里d是一个常数,c表示齐性流形的数量曲率.而且作为发展方程的应用,我们得到... 相似文献
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In this paper, we investigate Lie symmetry group, optimal system, exact solutions and conservation laws of modified hyperbolic geometric flow via Lie symmetry method. Then, conservation laws of modified hyperbolic geometric flow are obtained by applying Ibragimov method. 相似文献
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In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the(1 + n)-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyperbolic Yamabe problem; for the case of n = 2, 3, we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem;while for general multi-dimensional case n ≥ 2, we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem. 相似文献
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By means of the classical symmetry method,a hyperbolic Monge-Ampère equation is investigated.The symmetry group is studied and its corresponding group invariant solutions are constructed.Based on the associated vector of the obtained symmetry,the authors construct the group-invariant optimal system of the hyperbolic Monge-Ampère equation,from which two interesting classes of solutions to the hyperbolic Monge-Ampère equation are obtained successfully. 相似文献
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Kosov A. A. Semenov E. I. Tirskikh V. V. 《Journal of Applied and Industrial Mathematics》2021,15(2):253-260
Journal of Applied and Industrial Mathematics - We study the system of two fourth-order nonlinear hyperbolic partial differential equations. The right-hand sides of the equations contain double... 相似文献
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Ma Li & Wei Zheng 《偏微分方程(英文版)》2023,36(1):48-57
In this paper, we study the discrete Morse flow for either Yamabe type heat flow or nonlinear heat flow on a bounded regular domain in the whole space. We show that under suitable assumptions on the initial data $g$ one has a weak approximate discrete Morse flow for the Yamabe type heat flow on any time interval. This phenomenon is very different from the smooth Yamabe flow, where the finite time blow up may exist. 相似文献
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In this paper, we construct spherically symmetric solutions of the equations of compressible flow, which are important in the theory of explosion waves in air, water, and other media. Following McVittie [ 1 ], we write a general solution form, in terms of velocity potential, as a product of a function of time and a function of a similarity variable. First, we find solutions to the equations of motion and continuity without reference to adiabatic or isentropic relation. These solutions are quite general and can be applied to nonadiabatic motions, such as the motions of interstellar gas clouds that lose energy by radiation. All the solutions found by McVittie [ 1 ] have linear velocity profile with respect to distance. We introduce a nonlinear form of the velocity function containing an arbitrary function of the similarity variable. Adiabatic conditions lead to a second-order ODE, which we discuss in some detail. We relate our work to the earlier investigations of Taylor [ 2 ], McVittie [ 1 ], and Keller [ 3 ]. 相似文献
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Qi S. Zhang 《Geometriae Dedicata》2003,101(1):153-165
We prove the existence of positive, finite energy solutions to the Yamabe equation
on some noncompact manifolds with positive scalar curvature. We also clarify a published result on the existence of 'complete solutions' on those manifolds. 相似文献
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拟线性双曲型方程(组)的精确能控性 总被引:1,自引:0,他引:1
李大潜 《高校应用数学学报(A辑)》2005,20(2):127-146
本文为作者在中国科学院数学与系统科学研究院举办的第六届华罗庚数学讲座上的讲稿.§1 引言——从常微分方程谈起考虑如下的线性常微分方程组dXdt=AX+Bu,(1.1)其中,t为自变量(时间),X=(X1,…,XN)为状态变量,u=(u1,…,um)为控制变量,而A及B分别为N×N及N×m常数阵.(1.1)是一个有限维的动力系统.说该系统在时间区间[0,T](T>0)上具有精确能控性,是指对于在t=0时任意给定的初值X0及在t=T时任意给定的终值XT,一定能找到[0,T]上的控制函数u=u(t),使Cauchy问题dXdt=AX+Bu(t),(1.2)t=0:X=X0(1.3)的解X=X(t)精确地满足终端条件t=T:X=X… 相似文献