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21.
Shouming Zhou 《Mathematical Methods in the Applied Sciences》2017,40(10):3718-3732
This paper deals with the non‐uniform dependence and persistence properties for a coupled Camassa–Holm equations. Using the method of approximate solutions in conjunction with well‐posedness estimate, it is proved that the solution map of the Cauchy problem for this coupled Camassa–Holm equation is not uniformly continuous in Sobolev spaces Hs with s > 3/2. On the other hand, the persistence properties in weighted Lp spaces for the solution of this coupled Camassa–Holm system are considered. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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This paper deals with the Cauchy problem for a shallow water equation with high-order nonlinearities, y t +u m+1 y x +bu m u x y=0, where b is a constant, $m\in \mathbb{N}$ , and we have the notation $y:= (1-\partial_{x}^{2}) u$ , which includes the famous Camassa–Holm equation, the Degasperis–Procesi equation, and the Novikov equation as special cases. The local well-posedness of strong solutions for the equation in each of the Sobolev spaces $H^{s}(\mathbb{R})$ with $s>\frac{3}{2}$ is obtained, and persistence properties of the strong solutions are studied. Furthermore, although the $H^{1}(\mathbb{R})$ -norm of the solution to the nonlinear model does not remain constant, the existence of its weak solutions in each of the low order Sobolev spaces $H^{s}(\mathbb{R})$ with $1<s<\frac{3}{2}$ is established, under the assumption $u_{0}(x)\in H^{s}(\mathbb{R})\cap W^{1,\infty}(\mathbb{R})$ . Finally, the global weak solution and peakon solution for the equation are also given. 相似文献
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Nonlinear Dynamics - This paper studies the exponential cluster synchronization problem of complex dynamical networks with delayed couplings and nonidentical nodes. A new type of pinning impulsive... 相似文献
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Junkang Tian Yongming LiJinzhou Zhao Shouming Zhong 《Applied mathematics and computation》2012,218(9):5769-5781
In this paper, the problem of stochastic stability criterion of Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates is considered. Some new delay-dependent stability criteria are derived by choosing a new class of Lyapunov functional. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. 相似文献
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Shouming Zhou 《Journal of Evolution Equations》2014,14(3):727-747
This paper deals with the Cauchy problem for a cross-coupled Camassa–Holm equation $$m_t=-(vm)_x-mv_x, n_t=-(un)_x-nu_x,$$ where \({n\doteq v-v_{xx}}\) , \({m\doteq u-u_{xx}+\omega}\) with a constant ω. The local well-posedness of solutions for the Cauchy problem of the cross-coupled Camassa–Holm equation in Sobolev space \({H^s(\mathbb{R})}\) with s > 5/2 is established. Under some assumptions, the existence and uniqueness of the global solutions to the equation are shown, and the blowup scenario of the solutions to the equation is also obtained. 相似文献
30.
Shouming Zhou Chunlai Mu Rong Zeng 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2011,62(3):483-493
This paper deals with the quenching phenomenon for a non-local diffusion equation $$u_t(x,t)=\int\limits_\Omega{J(x-y)(u(y,t)-u(x,t))}{\rm d}y-f(u(x,t)),(x,t)\in\Omega\times[0,T),$$ with a general singular absorption term and Neumann boundary condition. The local existence and uniqueness of the solution are proved, and the solution of the equation quenches in finite time is shown. Moreover, under appropriate condition, the only quenching point is x?=?0, and the estimate of the quenching rate is obtained. Finally, some numerical experiments are performed, which illustrate our results. 相似文献