The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for...The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.展开更多
In this paper, we study fully discrete spectral method and long time behavior of solution of generalized Kuramoto-Sivashinsky equation with periodic initial condition. We prove that the large time error estimation fo...In this paper, we study fully discrete spectral method and long time behavior of solution of generalized Kuramoto-Sivashinsky equation with periodic initial condition. We prove that the large time error estimation for fully discrete solution of spectral method. We prove the existence of approximate attractors AN, ANk respectively and d(AN, A) → 0, d(ANk, A) → 0.展开更多
The computation of Hopf bifurcation points for differential equations with a parameter α is considered. It is well known that the Hopf bifurcation is well characterized by the fact that the first (largest) Lyapunov e...The computation of Hopf bifurcation points for differential equations with a parameter α is considered. It is well known that the Hopf bifurcation is well characterized by the fact that the first (largest) Lyapunov exponent is zero and the rest are not zero, or by the fact that the corresponding Jacobian has two purely imaginary roots which cross the imaginary axis as α increases through some α 0. An algorithm for detecting Hopf bifurcation points is given in this paper.The basic ideas and techniques are exemplified for the Kuramoto Sivashinsky equations. These equations are chosen because they are fairely simple while the dynamics is sufficiently complicated.展开更多
The new analytical travelling wave solutions to the generalized Kuramoto Sivashinsky (K S) equation were obtained by introducing a special transformation.
In this paper, a linearized three level difference scheme is derived for two-dimensional model of an alloy solidification problem called Sivashinsky equation. Further, it is proved that the scheme is uniquely solvable...In this paper, a linearized three level difference scheme is derived for two-dimensional model of an alloy solidification problem called Sivashinsky equation. Further, it is proved that the scheme is uniquely solvable and convergent with convergence rate of order two in a discrete L<sup>∞</sup>-norm. At last, numerical experiments are carried out to support the theoretical claims.展开更多
The generialized Kuramoto Sivashinski equation and Fisher equation in chemical reaction diffusion was studied in this paper. By introducing a new method, the anthors obtained the exact traveling wave solution for th...The generialized Kuramoto Sivashinski equation and Fisher equation in chemical reaction diffusion was studied in this paper. By introducing a new method, the anthors obtained the exact traveling wave solution for the two types of reaction diffusion equations.展开更多
文摘The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.
基金Supported by the National Fund of Natueal Sciences and by Science and Technology Fund ofShanghai Higher Education
文摘In this paper, we study fully discrete spectral method and long time behavior of solution of generalized Kuramoto-Sivashinsky equation with periodic initial condition. We prove that the large time error estimation for fully discrete solution of spectral method. We prove the existence of approximate attractors AN, ANk respectively and d(AN, A) → 0, d(ANk, A) → 0.
文摘The computation of Hopf bifurcation points for differential equations with a parameter α is considered. It is well known that the Hopf bifurcation is well characterized by the fact that the first (largest) Lyapunov exponent is zero and the rest are not zero, or by the fact that the corresponding Jacobian has two purely imaginary roots which cross the imaginary axis as α increases through some α 0. An algorithm for detecting Hopf bifurcation points is given in this paper.The basic ideas and techniques are exemplified for the Kuramoto Sivashinsky equations. These equations are chosen because they are fairely simple while the dynamics is sufficiently complicated.
文摘The new analytical travelling wave solutions to the generalized Kuramoto Sivashinsky (K S) equation were obtained by introducing a special transformation.
文摘In this paper, a linearized three level difference scheme is derived for two-dimensional model of an alloy solidification problem called Sivashinsky equation. Further, it is proved that the scheme is uniquely solvable and convergent with convergence rate of order two in a discrete L<sup>∞</sup>-norm. At last, numerical experiments are carried out to support the theoretical claims.
文摘The generialized Kuramoto Sivashinski equation and Fisher equation in chemical reaction diffusion was studied in this paper. By introducing a new method, the anthors obtained the exact traveling wave solution for the two types of reaction diffusion equations.
