scholarly journals EXISTENCE AND NON-EXISTENCE OF GLOBAL SOLUTIONS FOR THE SEMILINEAR COMPLEX GINZBURG-LANDAU TYPE EQUATION IN HOMOGENEOUS AND ISOTROPIC SPACETIME

2021 ◽  
Vol 75 (2) ◽  
pp. 169-209
Author(s):  
Makoto NAKAMURA ◽  
Yuya SATO
Keyword(s):  
Type Equation ◽  
Global Solutions ◽  
Ginzburg Landau

scholarly journals Cauchy problem for the complex Ginzburg-Landau type Equation with $L^{p}$-initial data

2014 ◽  
Vol 139 (2) ◽  
pp. 353-361 ◽  
Author(s):  
Daisuke Shimotsuma ◽  
Tomomi Yokota ◽  
Kentarou Yoshii
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Type Equation ◽  
Ginzburg Landau

scholarly journals ASYMPTOTIC BEHAVIOR OF BLOWUP SOLUTIONS FOR ELLIPTIC EQUATIONS WITH EXPONENTIAL NONLINEARITY AND SINGULAR DATA

2009 ◽  
Vol 11 (03) ◽  
pp. 395-411 ◽  
Author(s):  
LEI ZHANG
Keyword(s):  
Elliptic Equations ◽  
Type Equation ◽  
Global Solutions ◽  
Order Elliptic Equation ◽  
Liouville Type ◽  
Exponential Nonlinearity ◽  
Second Order Elliptic Equation ◽  
Singular Data ◽  
Sharp Error ◽  
Uniformly Bounded

We consider a sequence of blowup solutions of a two-dimensional, second-order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of Bartolucci–Chen–Lin–Tarantello, it is proved that the profile of the solutions differs from global solutions of a Liouville-type equation only by a uniformly bounded term. The present paper improves their result and establishes an expansion of the solutions near the blowup points with a sharp error estimate.

scholarly journals On Global Solutions for the Cauchy Problem of a Boussinesq-Type Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Hatice Taskesen ◽  
Necat Polat ◽  
Abdulkadir Ertaş
Keyword(s):  
Cauchy Problem ◽  
Initial Value Problem ◽  
Type Equation ◽  
Global Solutions ◽  
Initial Energy ◽  
Potential Well ◽  
Global Weak Solutions ◽  
Power Type ◽  
Initial Value ◽  
The Cauchy Problem

We will give conditions which will guarantee the existence of global weak solutions of the Boussinesq-type equation with power-type nonlinearity and supercritical initial energy. By defining new functionals and using potential well method, we readdressed the initial value problem of the Boussinesq-type equation for the supercritical initial energy case.

scholarly journals Global existence for the generalised 2D Ginzburg-Landau equation

2003 ◽  
Vol 44 (3) ◽  
pp. 381-392 ◽  
Author(s):  
Hongjun Gao ◽  
Keng-Huat Kwek
Keyword(s):  
Existence And Uniqueness ◽  
Landau Equation ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Ginzburg Landau ◽  
Spatial Variables ◽  
Type Complex ◽  
Ginzburg Landau Equation ◽  
Fifth Order ◽  
Formation Systems

AbstractGinzburg-Landau type complex partial differential equations are simplified mathematical models for various pattern formation systems in mechanics, physics and chemistry. Most work so far has concentrated on Ginzburg-Landau type equations with one spatial variable (1D). In this paper, the authors study a complex generalised Ginzburg-Landau equation with two spatial variables (2D) and fifth-order and cubic terms containing derivatives. Based on detail analysis, sufficient conditions for the existence and uniqueness of global solutions are obtained.

scholarly journals Absence of global solutions of a mixed problem for a Ginzburg–Landau type nonline-ar evolution equation

2019 ◽  
Vol 484 (2) ◽  
pp. 147-149
Author(s):  
Sh. M. Nasibov
Keyword(s):  
Initial Data ◽  
Evolution Equation ◽  
Mixed Problem ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Global Solutions ◽  
Ginzburg Landau

We study the problem of the absence of global solutions of the first mixed problem for one nonlinear evolution equation of Ginzburg–Landau type.We prove that global solutions of the studied problem are absent for “sufficiently large” values of the initial data.

scholarly journals Traveling wave solutions and its stability for 3D Ginzburg-Landau type equation

2011 ◽  
Vol 16 (2) ◽  
pp. 507-527
Author(s):  
Shujuan Lü ◽  
◽  
Chunbiao Gan ◽  
Baohua Wang ◽  
Linning Qian ◽  
...  
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Type Equation ◽  
Ginzburg Landau ◽  
Wave Solutions

Remarks on nonminimizing solutions of a Ginzburg–Landau type equation

1996 ◽  
Vol 13 (2) ◽  
pp. 199-215 ◽  
Author(s):  
Myriam Comte ◽  
Petru Mironescu
Keyword(s):  
Type Equation ◽  
Ginzburg Landau

Dynamics of a Higher-Order Ginzburg–Landau-Type Equation

2021 ◽  
pp. 187-207
Author(s):  
Theodoros P. Horikis ◽  
Nikos I. Karachalios ◽  
Dimitrios J. Frantzeskakis
Keyword(s):  
Type Equation ◽  
Higher Order ◽  
Ginzburg Landau
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