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非线性泛函分析与无穷维动力系统中相关理论及应用问题的研究
  • 项目名称：非线性泛函分析与无穷维动力系统中相关理论及应用问题的研究
  • 项目类别：重点项目
  • 批准号：11031003
  • 申请代码：A0106
  • 项目来源：国家自然科学基金
  • 研究期限：2011-01-01-2014-12-31
  • 项目负责人：钟承奎
  • 负责人职称：教授
  • 依托单位：南京大学
  • 批准年度：2010
中文摘要：

本项目主要研究无穷维动力系统全局吸引子存在性，无穷维动力系统平衡点和多重平衡点的存在性，平衡点附近的动力学行为以及无穷维动力系统的正则逼近三个方面的问题.重点研究在低正则外力项作用下非线性发展型方程的全局吸引子包括一致吸引子和拉回吸引子的存在性；研究3D等熵，非等熵可压缩的Navier-Stokes(-poisson)(-Fourier)方程组（非）自治系统的轨道吸引子的存在性等；以半线性抛物型方程，半线性Schrodinger方程等为背景,重点研究具有或不具有Lyaponuv泛函的无穷维动力系统的平衡点的存在性,多重性，研究平衡点的稳定流形，不稳定流形以及中心流形等;以半线性抛物型方程，半线性波方程等为背景重点研究发展型方程的正则逼近问题.

中文主题词： Schrodinger方程；Lyaponov 指数；行波解；全局吸引子；谱
英文摘要：

Schrodinger equation；Lyapunov index；Travelling wave equation；Global attractor；Spectrum

英文主题词： Schrodinger equation；Lyapunov index；Travelling wave equation；Global attractor；Spectrum
结论摘要：

本项目主要研究无穷维动力系统的长时间的渐近行为。在准周期Schrodinger算子谱，带拟周期位势的 Schrodinger 算子的谱问题，Liapunov指数连续性与正则性问题，非线性非局部反应扩散方程的行波解与稳态解问题，非线性反应扩散方程，非线性波方程，以及流体力学中几个重要方程的全局吸引子存在性问题与全局吸引子维数问题的研究中，取得了一批重要研究成果，取得了项目的预期成果。本项目在执行期间，共发表研究论文70多篇，其中在 Invent. Math.（1篇）,Advances in Mathematics（1篇）, Duke Math. J.（ 1篇）J. Differential Equations（12篇），Trans. Amer. Math. Soc.（1篇），Comm. Math. Phys.（2篇） Discrete Contin. Dyn. Syst.B (7篇), Nonlinear Analysis TMA以及RWA（14篇），等有影响的期刊上发表论文30多篇，由Springer出版集团Birkhauser出版社出版的学术专著1部（ISBN: 978-3-0348-0279-6)。

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 45
  • 0
  • 0
  • 0
  • 1
期刊论文
Global existence and exponential stability of solutions to the one-dimensional full non-Newtonian fl
Long-time behavior of a quasilinear viscoelastic equation with past history,
The Cauchy problem for a 1D compressible viscous micropolar fluid model: Analysis of the stabilizati
Global Attractors for p-Laplacian Equations with Dynamic Flux Boundary Conditions
Large-time behavior of solutions for the one-dimensional infrarelativistic model of a compressible v
Global Existence, Asymptotic behavior and uniform attractor for a non-autonomous equation
Upper Semicontinuity of pullback attractors for a non-autonomous viscoelastic equation
Remarks on global smooth solutions to a 1D self-gravitating viscous radiative and reactive gas
General decay for a system of nonlinear viscoelastic wave equations with weak damping
Analysis of the viscous Cahn-Hilliard equation in RN
Global attractors for the p-Laplacian equations with nonregular data
Examples of discontinuity of Lyapunov exponent in smooth quasiperiodic cocycles.
Reducibility of slow quasi-periodic linear systems.
Effect of cross-diffusion on the stationary problem of a diffusive competition model with a protecti
Stability of traveling waves in a monostable delayed system without quasi-monotonicity
Pullback attractors for three-dimensional Navier-Stokes-Voigt equations with delays
Global existence and uniform decay for the one-dimensional model of thermodiffusion with second soun
Uniform attractors for non-autonomous thermodiffusion equations
Periodic pyramidal traveling fronts of bistable reaction-diffusion equations with time-periodic nonl
Traveling wave solutions of a competitive recursion,
Averaging of a 3D Navier–Stokes–Voight equation with singularly oscillating forc
Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable non
Pulsating type entire solutions of monostable reaction advection-diffusion equations in periodic exc
Long-time behavior of solutions to nonlinear reaction diffusion equations involving L1data.
Persistence of bistableWaves in a delayed population model with stage structure on a two-dimensional
Pullback attractors for the non-autonomous Benjamin-Bona-Mahony equations in H2,
Global existence, asymptotic stability and uniform attractors for non-autonomous thermoelastic syste
UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR NONAUTONOMOUS KIRCHHOFF WAVE MODELS
A KAM theorem for higher dimensional nonlinear Schrödinger equations.
Effects of cross-diffusion and heterogeneous environment on positive steady states of a prey&nda
具有动力边界的非自治p-拉普拉斯方程解的适定性
Pullback Attractors for Semi-uniformly Dissipative Dynamical Systems
一类退化抛物方程全局吸引子的正则性
Schauder边界条件的推广及多临界点定理
Traveling waves in a nonlocal dispersal Kermack-Mckendrick epidemic model
Entire solutions in lattice delayed differential equations with nonlocal interaction: Bistable case
Stability and Hopf bifurcation for a three-component reaction-diffusion population model with delay
Spatial patterns of the Holling-Tanner predator-prey model with nonlinear diffusion effects
Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems..
Global existence and asymptotic behavior of solutions for thermodiffusion equations
Bifurcation analysis on a diffusive Holling-Tanner predator-prey model
Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Ap
Global existence and exponential stability for a 1D compressible and radiative MHD flow
著作
Global Wellposedness of Nonlinear Parabolic-Hyperbolic Coupled Systems
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