非自治耗散Zakharov无穷格点系统的渐近行为.pdfVIP

Abstract Infinite dimensional dynamical systems play an very important role in nonlinear science. Lattice systems are a kind of very important infinite dimensional dynam- ical systems. Kernel section(including global attractor) is that of central parts in studying infinite dimensional dynamical systems. The research on the kernel section lies in two aspects. one aspect is it’s existence, the other is it’s properties, such as the Kolmogorov entropy, Hausdorff dimension and upper continuity and so on. This master thesis focuses on research on the the compact kernel section for a kind of infinite lattice systems such as nonautonomouse dissapitive Zakharov infinite lattice system. Firstly, the author introduce the development survey and main research directions of dynamical systems and the author’s research works. In Chapter 2, the author briefly introduce preliminary results and definitions, the Sobolev function spaces and frequently used inequalities such as Young’s Inequality and Gronwall’s Inequality. In this aspect, the author studied a kind of lattice systems on the basis of the theoretic frame of infinite dimensional dynamic systems by V. V. Chepyzhov, M. I. Vishik. The author studied nonautonomous dissipative Zakharov lattice systems. By introducing a new weight inner product and norm in the space and establishing uniform estimate on “ Tail End” of solutions, the author overcome some difficulties raised by the lack of Sobolev compact embedding in the case of unbounded domains, and prove the existence of the compact kernel sections; By using the element decom- position and the covering property of a polyhedron by balls in the finite dimensional space, and then the author make an estimates of the Kolmogorov ǫ-entropy for the compact kernel sections and obtain upper bounds; finally, the author present the upper semiconti