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  • 1
    Electronic Resource
    Electronic Resource
    Global smooth solution for the Klein–Gordon–Zakharov equations (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 4119-4124 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper the initial value problem to the Klein–Gordon–Zakharov equations in two dimensions is discussed. Without assuming that the Cauchy data are small, we prove the existence and uniqueness of the global smooth solution for the problem via the so-called continuous method and delicate a priori estimates. Also the asymptotic behaviour of the solution to the K–G–Z equations with a small parameter approaching zero is studied. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530950
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  • 2
    Electronic Resource
    Electronic Resource
    Long time behavior for the equation of finite-depth fluids (1994)
    Springer
    Communications in mathematical physics 163 (1994), S. 1-15 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In this paper we study the Cauchy problem for the generalized equation of finite-depth fluids $$\partial _t u - G(\partial _x^2 u) - \partial _x \left( {\frac{{u^p }}{p}} \right) = 0$$ whereG(·) is a singular integral, andp is an integer larger than 1. We obtain the long time behavior of the fundamental solution of linear problem, and prove that the solutions of the nonlinear problem with small initial data for $$p 〉 5/2 + \sqrt {21} /2$$ are decay in time and freely asymptotic to solutions of the linear problem. In addition we also study some properties of the singular integralG(·) inL q(R) withq〉1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02101732
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  • 3
    Electronic Resource
    Electronic Resource
    A class of general systems of KdV type I (1984)
    Springer
    Acta mathematicae applicatae sinica 1 (1984), S. 153-162 
    Details
    ISSN: 1618-3932
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider some wide class of general systems of Korteweg-de Vries equations which contain nonlinear terms with derivatives of higher order, we have proved the existence of generalized solution for this system and the asymptotic behavior ast→∞ and “blow up” property of the solution are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01669676
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  • 4
    Electronic Resource
    Electronic Resource
    The fractal structure of attractor for the generalized Kuramoto-Sivashinsky equations (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 263-277 
    Details
    ISSN: 1573-2754
    Keywords: GKS equation ; attractor ; inertial set ; fractal structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the generalized Kuramoto-Sivashinsky equations (GKS) with periodic initial boundary value problem are considered and the construction of inertial sets in space H2 is given. Furthermore, this paper gives and proves the fractal structure of attractors for GKS equations, and find out an exponentially approximating sequence of compact fractal localizing sets of the attractors, these results sharpen and improve the conclusions of the inertial sets and attractor for GKS equation in [1, 3, 5, 7], which describe a kind of geometrical structure of the attractors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02453391
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  • 5
    Electronic Resource
    Electronic Resource
    On the suitable weak solutions to the Boussinesq equations in a bounded domain (1996)
    Springer
    Acta mathematica sinica 12 (1996), S. 205-216 
    Details
    ISSN: 1439-7617
    Keywords: Initial-boundary value ; Existence ; Boussinesq equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we construct the suitable weak solution for the initial-boundary value problem of the Boussinesq equations and obtain some properties for these solutions. Also in the case of a two dimensional space the uniqueness of weak solution is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02108163
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  • 6
    Electronic Resource
    Electronic Resource
    Global attractors for the initial value problems of Cohn-Hilliard equations on compact manifolds (1996)
    Springer
    Acta mathematica sinica 12 (1996), S. 314-325 
    Details
    ISSN: 1439-7617
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we establish some theorems which are concerned with the equivalent norms of Sobolev spaces on a Riemannian manifold. Using the theorems we prove the existence of global attractors for the initial value problem of Cahn-Hilliard equations. The estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors are also obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02106985
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  • 7
    Electronic Resource
    Electronic Resource
    Global smooth solution for a coupled non-linear wave equations (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 419-425 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, the global existence and uniqueness of smooth solution to the initial-value problem for coupled non-linear wave equations are studied using the method of a priori estimates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140606
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  • 8
    Electronic Resource
    Electronic Resource
    The Global Attractors for the Periodic Initial Value Problem For a Coupled Non-linear Wave Equation (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 131-144 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of global attractors of the periodic initial value problem for a coupled non-linear wave equation is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of uniform a priori estimates for time.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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