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881.
The paper is devoted to a rigorous construction of a parabolic system of partial differential equations which displays space–time
chaotic behavior in its global attractor. The construction starts from a periodic array of identical copies of a temporally
chaotic reaction-diffusion system (RDS) on a bounded domain with Dirichlet boundary conditions. We start with the case without
coupling where space–time chaos, defined via embedding of multi- dimensional Bernoulli schemes, is easily obtained. We introduce
small coupling by replacing the Dirichlet boundary conditions by strong absorption between the active islands. Using hyperbolicity
and delicate PDE estimates we prove persistence of the embedded Bernoulli scheme. Furthermore we smoothen the nonlinearity
and obtain a RDS which has polynomial interaction terms with space and time-periodic coefficients and which has a hyperbolic
invariant set on which the dynamics displays spatio-temporal chaos. Finally we show that such a system can be embedded in
a bigger system which is autonomous and homogeneous and still contains space–time chaos. Obviously, hyperbolicity is lost
in this step.
Research partially supported by the INTAS project Attractors for Equations of Mathematical Physics, by CRDF and by the Alexander von Humboldt–Stiftung. 相似文献
882.
Hans Triebel 《Mathematische Nachrichten》2015,288(8-9):1057-1072
The paper deals with global solutions of Navier‐Stokes equations with infrared‐damped initial data in the context of Haar wavelets and function spaces of type where . 相似文献
883.
Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear Volterra difference equations in phase spaces. In particular, this gives a solution to an open problem posed very recently by E. Braverman and I. M. Karabash in Journal of Difference Equations and Applications 18 , 909–939 (2012). As an application, we apply the obtained results to study asymptotic behavior of equilibriums of discrete time neural networks. 相似文献
884.
We characterize boundedness, compactness and weak compactness of Volterra operators acting between different weighted Banach spaces of entire functions with sup‐norms in terms of the symbol g; thus we complement recent work by Bassallote, Contreras, Hernández‐Mancera, Martín and Paul 3 for spaces of holomorphic functions on the disc and by Constantin and Peláez 16 for reflexive weighted Fock spaces. 相似文献
885.
Simon P. Eveson Vladimir D. Stepanov Elena P. Ushakova 《Mathematische Nachrichten》2015,288(8-9):877-897
An embedding inequality of Sobolev type is characterized in the paper with help of a duality principle and boundedness criteria for the Hardy–Steklov integral operator in weighted Lebesgue spaces. 相似文献
886.
We prove a Desch‐Schappacher type perturbation theorem for strongly continuous and locally equicontinuous one‐parameter semigroups which are defined on a sequentially complete locally convex space. 相似文献
887.
Hédy Attouch Guillaume Garrigos Xavier Goudou 《Journal of Mathematical Analysis and Applications》2015
In a general Hilbert framework, we consider continuous gradient-like dynamical systems for constrained multiobjective optimization involving nonsmooth convex objective functions. Based on the Yosida regularization of the subdifferential operators involved in the system, we obtain the existence of strong global trajectories. We prove a descent property for each objective function, and the convergence of trajectories to weak Pareto minima. This approach provides a dynamical endogenous weighting of the objective functions, a key property for applications in cooperative games, inverse problems, and numerical multiobjective optimization. 相似文献
888.
We consider a Dirichlet problem in a planar domain with a hole of diameter proportional to a real parameter ? and we denote by u? the corresponding solution. The behavior of u? for ? small and positive can be described in terms of real analytic functions of two variables evaluated at (?,1/log??). We show that under suitable assumptions on the geometry and on the boundary data one can get rid of the logarithmic behavior displayed by u? for ? small and describe u? by real analytic functions of ?. Then it is natural to ask what happens when ? is negative. The case of boundary data depending on ? is also considered. The aim is to study real analytic families of harmonic functions which are not necessarily solutions of a particular boundary value problem. 相似文献
889.
Vakhtang Kokilashvili Mieczysław Mastyło Alexander Meskhi 《Journal of Mathematical Analysis and Applications》2015
The main aim of this paper is to study a general multisublinear operators generated by quasi-concave functions between weighted Banach function lattices. These operators, in particular, generalize the Hardy–Littlewood and fractional maximal functions playing an important role in harmonic analysis. We prove that under some general geometrical assumptions on Banach function lattices two-weight weak type and also strong type estimates for these operators are true. To derive the main results of this paper we characterize the strong type estimate for a variant of multilinear averaging operators. As special cases we provide boundedness results for fractional maximal operators in concrete function spaces. 相似文献
890.
Helmut Rudolph 《Optimization》2015,64(8):1739-1757