共查询到19条相似文献,搜索用时 62 毫秒
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得到了双曲Yamabe流的一些精确解.第一类解是具有初始度量为Einstein的解,第二类解是具有轴对称的解.最后,作为这种流的特殊解,定义了稳定双曲Yamabe孤子,而且得到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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In this paper, weconsider the evolution of a soliton when dissipative lose exists. By means of non-perturbed method, an exact envelope wave solution of nonlimear Schroedinger equation with dissipative term is obtained. It is shown that when Г=γ0/(1 2γot), the solution given here still maintains the hyperbolic secant profile. 相似文献
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本文利用广义凸性方法证明了边界耗散的非线性四阶方程初边值问题整体解的不存在性 相似文献
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讨论具有非线性耗散项双曲系统的初值问题,对初值的模不加小性假设,而要求其一阶导数适当小情形下,证明其光滑解的整体存在性,并用经典解的特征线法获得解的模估计,同时应用极值原理得到解的偏导数的一致估计. 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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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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Yi ZHOU 《数学年刊B辑(英文版)》2011,32(5):771-780
The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic
systems. Under the assumption that the system is weakly dissipative, Hanouzet
and Natalini established the global existence of smooth solutions for small initial data (in
Arch. Rational Mech. Anal., Vol. 169, 2003, pp. 89–117). The aim of this paper is to give
a completely different proof of this result with slightly different assumptions. 相似文献
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Fanqi Zeng 《数学研究》2021,54(4):371-386
We introduce the concept $h$-almost Yamabe soliton which extends naturallythe almost Yamabe soliton by Barbosa-Ribeiro and obtain some rigidity results concerning $h$-almost Yamabe solitons. Some condition for a compact $h$-almost Yamabesoliton to be a gradient soliton is also obtained. Finally, we give some characterizations for a special class of gradient $h$-almost Yamabe solitons. 相似文献
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Yao-junYe 《应用数学学报(英文版)》2004,20(1):93-100
In this paper we show the decay of solutions to the initial-boundary value problem for somenonlinear hyperbolic equation with a nonlinear dissipative term,by using a difference inequality. 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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AClassofCauchyProblemforQuasilinearHyperbolicSystemswiththeWeaklyDissipativeTerms¥LiuFagui;YangQiao(NorthChinaInstituteofWate... 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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Exact Controllability for Nonautonomous First Order Quasilinear Hyperbolic Systems 总被引:2,自引:0,他引:2 下载免费PDF全文
Zhiqiang WANG 《数学年刊B辑(英文版)》2006,27(6):643-656
By means of the theory on the semi-global C1 solution to the mixed initial-boundary value problem (IBVP) for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomous first order quasilinear hyperbolic systems with general nonlinear boundary conditions. 相似文献
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This paper concerned with the classical solutions to system of one dimensional hydromagnetic dynamics with dissipative mechanism. Under certain hypotheses on the initial data, the global existence and the formation of singularities for classical solution are obtained. Our results show that the damping dissipation is strong enough to preserve the smoothness of the classical solution. 相似文献