郭柏灵院士三十多年来,潜心于非线性发展方程的理论研究,其中包括Landau-Lifshitz方程、Benjamin-one方程等,很多该类型的非线性发展方程都具有明显的实际背景,而且都有鲜明的特性,如强非线性耦合性和奇异性等。研究了这些方程大初值可解性、解的惟一性、正则性、渐近行为以及爆破现象等,完善了数学理论。
这套《郭柏灵论文集》按照郭老师在不同时期所从事的研究领域,分成多卷出版。文集中所搜集的都是郭老师正式发表过的学术成果。把这些成果整理成集出版,不仅系统地反映了他的科研成就,更重要的是对于从事这方面学习、研究的学者无疑大有裨益。本书为《郭柏灵论文集》的第五卷。
1998年
Partial Regularity for Two Dimensional Landau-Lifshitz Equations
Global Attractor of a Class of Strongly Damped Nonlinear Wave Equations
耦合Schrodinger-KdV 方程组Cauchy问题的适定性
Slow Time-periodic Solutions of Cubic-quintic Ginzburg-Landau Equation (I)
--Equilibria Problem
Slow Time-periodic Solutions of Cubic-quintic Ginzburg-Landau Equation (II)
--Heteroclinic Orbits
Attractors for the Long-short Wave Equations
Initial-boundary Value Problem for the Landau-Lifshitz System (I)
--Existence and Partial Regularity
Initial-boundary Value Problem for the Landau-Lifshitz System (II)
--Uniqueness
Gevrey Class Regularity and Approximate Inertial Manifolds for the Newton-Boussinesq Equations
Attractor for the Dissipative Generalized Klein-Gordon-Schr'odinger Equations
The Global Smooth Solution for Landau-Lifshitz-Maxwell Equation without Dissipation
Global Attractor and Its Dimension Estimates for the Generalized Dissipative KdV Equation on R
Attractor for the Dissipative Hamiltonian Amplitude Equation Governing Modulated Wave Instabilities
Long Time Behavior of Strongly Damped Nonlinear Wave Equations
Space-time Means and Solutions to a Class of Nonlinear Parabolic Equations
Orbital Stability of Solitary Waves of the Long Wave-short Wave Resonance Equations
Well-posedness of Cauchy Problem for Coupled System of Long-short Wave Equations
Global Flow Generated by Coupled System of Schrodinger-BBM Equations
Remarks on the Global Attractors of Semigroups Having a Lyapunov Functional
Approximate Inertial Manifolds of Non-Newtonian Viscous Incompressible Fluids
1999年
Long Time Behavior of Nonlinear Strain Waves in Elastic Waveguides
Smooth Solution for One-dimensional Inhomogeneous Heisenberg Chain Equations
Smooth Solution of the Generalized System of Ferromagnetic Chain
Well-posedness of the Cauchy Problem for the Coupled System of the Schrodinger-KdV Equations
The Cauchy Problem for Davey-Stewartson Systems
Solitary Waves for Two-dimensional Schr'6dinger-Kadomtsev-Petviashvili Equations
Global Existence of Smooth Solution to Nonlinear Thermoviscoelastic System with Clamped Boundary Conditions in Solid-like Materials
Asymptotic Behavior of the Solution to the System for a Viscous Reactive Gas
Long-time Uniform Stability of Solution to Magnetohydrodynamics Equation
Measure-valued Solution to the Strongly Degenerate Compressible Heisenberg Chain Equations
Orbital Stability of Solitary Waves of Coupled KdV Equations
2000年
三维Wigner-Poisson方程组的Cauchy问题
The Attractors for Landau-Lifshitz-Maxwell Equations
Global Attractor of Nonlinear Strain Waves in Elastic Waveguides
Initial-boundary Value Problem for the Unsaturated Landau-Lifshitz System
Exponential Attractors for the Generalized Ginzburg-Landau Equation
Global Existence of Solutions to the Derivative 2D Ginzburg-Landau Equation
Approximate Inertial Manifolds for Davey-Stewartson Equations
On the Weak Solution to the Equations of Antiferromagnets
Existence and Blow-up of Solutions to Degenerate Davey-Stewartson Equations
Initial-boundary Value Problem for the Landau-Lifshitz System with Applied Field
Algebraic L2 Decay for the Solution to a Class System of Non-Newtonian Fluid in R
Attractors for the Ginzburg-Landau-BBM Equations in an Unbounded Domain
2001年
具调和振子的非线性Schrodinger方程
Long Time Behavior of Solutions of Davey-Stewartson Equations
Neumann Problem for the Landau-Lifshitz-Maxwell System in Two Dimensions
Some Exact Nontrivial Global Solutions with Values in Unit Sphere for Two-dimensional Landau-Lifshitz Equations
Existence of the Periodic Solution for the Weakly Damped Schrodinger-Boussinesq Equation
Almost Periodic Solution of Generalized Ginzburg-Landau Equation
On the Initial Value Problem and Scattering of Solutions for the Generalized Davey-Stewartson Systems
三维Wigner-Poisson方程解的渐进性
The Global Solution for Landau-Lifshitz-Maxwell Equations
Time-periodic Solutions to the Ginzburg-Landau-BBM Equations
具非均匀介电常数的半导体方程组的初边值问题
后记