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排序方式: 共有78条查询结果,搜索用时 15 毫秒
1.
P.E. Kloeden 《Journal of Differential Equations》2008,244(8):2062-2090
The existence and uniqueness of a variational solution satisfying energy equality is proved for a semilinear heat equation in a non-cylindrical domain with homogeneous Dirichlet boundary condition, under the assumption that the spatial domains are bounded and increase with time. In addition, the non-autonomous dynamical system generated by this class of solutions is shown to have a global pullback attractor. 相似文献
2.
Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the
reaction-diffusion type is shown to have a unique stochastic stationary solution which pathwise attracts all other solutions.
A similar situation holds for each Galerkin approximation and each implicit Euler scheme applied to these Galerkin approximations.
Moreover, the stationary solution of the Euler scheme converges pathwise to that of the Galerkin system as the stepsize tends
to zero and the stationary solutions of the Galerkin systems converge pathwise to that of the evolution equation as the dimension
increases. The analysis is carried out on random partial and ordinary differential equations obtained from their stochastic
counterparts by subtraction of appropriate Ornstein-Uhlenbeck stationary solutions. 相似文献
3.
Classes of Runge–Kutta methods preserving the monotonicity of ordinary and delay differential equations are identified. Essentially, the vector b and the matrix A from the Butcher tableau should be such that all components of b are positive and all components of the matrix B(r)A, where B(r) is the inverse of the matrix I+rA, are nonnegative for sufficiently small positive r. The latter is satisfied by all explicit, diagonally-implicit and fully implicit Runge–Kutta methods for which all of the components of the matrix A, except those that are zero by definition, are positive. 相似文献
4.
P.E Kloeden 《Fuzzy Sets and Systems》1982,7(3):275-296
A fuzzy dynamical system on an underlying complete, locally compact metric state space X is defined axiomatically in terms of a fuzzy attainability set mapping on X. This definition includes as special cases crisp single and multivalued dynamical systems on X. It is shown that the support of such a fuzzy dynamical system on X is a crisp multivalued dynamical system on X, and that such a fuzzy dynamical system can be considered as a crisp dynamical system on a state space of nonempty compact fuzzy subsets of X. In addition fuzzy trajectories are defined, their existence established and various properties investigated. 相似文献
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6.
Phil Diamond Peter Kloeden Victor Kozyakin Alexei Pokrovskii 《Mathematische Nachrichten》1998,191(1):59-81
The finiteness of computer arithmetic can lead to some dramatic differences between the behaviour of a continuous dynamical system and a computer simulation. A thorough rigorous theoretical analysis of what may or what does happen is usually extremely difficult and to date little has been done even in relatively simple contexts. The comparative behaviour of a rotation mapping in the plane and on a uniform lattice in the plane is one such example. Simulations show that the rounding operator applied to a planar rotation mapping more or less preserves the qualitative behaviour of the original mapping, whereas the application of the truncation operator to a planar rotation can lead to quite different dynamical features. In this paper a theoretical justification of the properties of the planar rotation mappings under truncation to a, uniform integer lattice is provided, in particular properties of boundedness and dissipativity are investigated. 相似文献
7.
Higher-order implicit strong numerical schemes for stochastic differential equations 总被引:2,自引:0,他引:2
Higher-order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed. These are based on a stochastic Taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero. The regions of absolute stability of these implicit and related explicit methods are also examined. 相似文献
8.
H. R. Schneebeli P. E. Kloeden 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(1):176-178
Ohne Zusammenfassung 相似文献
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