𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Initial-Value Problem for the Generalized Two-Dimensional Ginzburg–Landau Equation

✍ Scribed by Hongjun Gao; Jinqiao Duan

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
198 KB
Volume
216
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

The Ginzburg᎐Landau-type complex partial differential equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. Most work so far concentrates on Ginzburg᎐Landau-type equations Ž . with one spatial dimension 1D . In this paper, the authors study a complex Ž . generalized Ginzburg᎐Landau equation with two spatial dimensions 2D . Sufficient conditions for the existence and uniqueness of global solutions for the initial-value problem of the generalized 2D Ginzburg᎐Landau equation are obtained. This rigorously establishes the foundation for further investigation of this type of model.

📜 SIMILAR VOLUMES

Asymptotics for the Generalized Two-Dime
Asymptotics for the Generalized Two-Dimensional Ginzburg–Landau Equation
✍ Hongjun Gao; Guoguang Lin; Jinqiao Duan 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 198 KB

In this paper, the authors have studied a generalized Ginzburg᎐Landau equation Ž . in two spatial dimensions 2D . They have shown that this equation, under periodic boundary conditions, has the maximal attractor with finite Hausdorff dimension. This rigorously establishes the foundation for further

The initial boundary value problem for t
The initial boundary value problem for the Schröudinger equation
✍ Leif Abrahamsson; Heinz-Otto Kreiss 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 243 KB

## Abstract We study the stability properties of the one‐dimensional Schrödinger equation with boundary conditions that involve the derivative in the direction of propagation (or time). We show that this type of boundary condition might cause a strong growth of the amplitude of the solution. Such a

On the nonlinear stability of plane wave
On the nonlinear stability of plane waves for the ginzburg-landau equation
✍ Todd Kapitula 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 406 KB 👁 1 views

1 consider the nonlinear stability of plane wave solutions to a Ginzburg-Landau equation with additional fifth-order terms and cubic terms containing spatial derivatives. 1 show that, under the constraint that the diffusion coefficient be real, these waves are stable. Furthermore, it is shown that t