scholarly journals On some sufficient conditions for the blow-up solutions of the nonlinear Ginzburg-Landau-Schrödinger evolution equation

2004 ◽  
Vol 2004 (1) ◽  
pp. 23-35 ◽  
Author(s):  
Sh. M. Nasibov
Keyword(s):  
Boundary Condition ◽  
Euclidean Space ◽  
Initial Data ◽  
Evolution Equation ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Homogeneous Boundary Condition ◽  
Dimensional Euclidean Space ◽  
Ginzburg Landau ◽  
The Given

Investigation of the blow-up solutions of the problem in finite time of the first mixed-value problem with a homogeneous boundary condition on a bounded domain ofn-dimensional Euclidean space for a class of nonlinear Ginzburg-Landau-Schrödinger evolution equation is continued. New simple sufficient conditions have been obtained for a wide class of initial data under which collapse happens for the given new values of parameters.

Complete blow-up for quasilinear degenerate parabolic equations

2000 ◽  
Vol 130 (4) ◽  
pp. 877-908 ◽  
Author(s):  
R. Suzuki
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equation ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Image Position

Non-negative post-blow-up solutions of the quasilinear degenerate parabolic equation in RN (or a bounded domain with Dirichlet boundary condition) are studied. Various sufficient conditions for complete blow-up of solutions are given.

scholarly journals Blow-Up of Solutions with High Energies of a Coupled System of Hyperbolic Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Jorge A. Esquivel-Avila
Keyword(s):  
Initial Data ◽  
Blow Up ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Coupled System ◽  
Initial Energy ◽  
Evolution System ◽  
High Energies ◽  
Second Order In Time

We consider an abstract coupled evolution system of second order in time. For any positive value of the initial energy, in particular for high energies, we give sufficient conditions on the initial data to conclude nonexistence of global solutions. We compare our results with those in the literature and show how we improve them.

On Bäcklund transformation and vortex filament equation for pseudo null curves in Minkowski 3-space

2016 ◽  
Vol 13 (06) ◽  
pp. 1650077 ◽  
Author(s):  
Milica Grbović ◽  
Emilija Nešović
Keyword(s):  
Evolution Equation ◽  
Bäcklund Transformation ◽  
Sufficient Conditions ◽  
Vortex Filament ◽  
Backlund Transformation ◽  
Burger's Equation ◽  
Null Curve ◽  
Vortex Filament Equation ◽  
Null Curves ◽  
The Given

In this paper, we introduce Bäcklund transformation of a pseudo null curve in Minkowski 3-space as a transformation mapping a pseudo null helix to another pseudo null helix congruent to the given one. We also give the sufficient conditions for a transformation between two pseudo null curves in the Minkowski 3-space such that these curves have equal constant torsions. By using the Da Rios vortex filament equation, based on localized induction approximation (LIA), we derive the vortex filament equation for a pseudo null curve and prove that the evolution equation for the torsion is the viscous Burger’s equation. As an application, we show that pseudo null curves and their Frenet frames generate solutions of the Da Rios vortex filament equation.

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.

Semi-E-Preinvex Functions

2012 ◽  
pp. 677-683
Author(s):  
Yu-Ru Syau ◽  
E. Stanley Lee
Keyword(s):  
Nonlinear Programming ◽  
Euclidean Space ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Dimensional Euclidean Space ◽  
Quasiconvex Functions ◽  
Invex Set ◽  
Preinvex Functions ◽  
The Relationship ◽  
Class Of Functions

A class of functions called semi-E-preinvex functions is defined as a generalization of semi-E-convex functions. Similarly, the concept of semi-E-quasiconvex functions is also generalized to semi-E-prequasiinvex functions. Properties of these proposed classes are studied, and sufficient conditions for a nonempty subset of the n-dimensional Euclidean space to be an E-convex or E-invex set are given. The relationship between semi-E-preinvex and E-preinvex functions are discussed along with results for the corresponding nonlinear programming problems.

Semi-E-Preinvex Functions

2010 ◽  
Vol 1 (3) ◽  
pp. 31-39
Author(s):  
Yu-Ru Syau ◽  
E. Stanley Lee
Keyword(s):  
Nonlinear Programming ◽  
Euclidean Space ◽  
Nonempty Subset ◽  
Sufficient Conditions ◽  
Dimensional Euclidean Space ◽  
Quasiconvex Functions ◽  
Invex Set ◽  
Preinvex Functions ◽  
The Relationship ◽  
Class Of Functions

A class of functions called semi--preinvex functions is defined as a generalization of semi--convex functions. Similarly, the concept of semi--quasiconvex functions is also generalized to semi--prequasiinvex functions. Properties of these proposed classes are studied, and sufficient conditions for a nonempty subset of the -dimensional Euclidean space to be an -convex or -invex set are given. The relationship between semi--preinvex and -preinvex functions are discussed along with results for the corresponding nonlinear programming problems.

scholarly journals EXISTENCE AND BLOW UP FOR A NONLINEAR VISCOELASTIC HYPERBOLIC PROBLEM WITH VARIABLE EXPONENTS

2020 ◽  
pp. 647
Author(s):  
Fatima Z. Mahdi ◽  
Ali Hakem
Keyword(s):  
Initial Data ◽  
Existence Theorem ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Variable Exponents ◽  
Hyperbolic Problem ◽  
Nonlinear Viscoelastic

 Our aim in this paper is to establish the weak existence theorem andfind under suitable assumptions sufficient conditions on $m, p$ andthe initial data for which the blow up takes place for the followingboundary value problem:$$|u_t|^{\rho}u_{tt}-\Delta u-\Deltau_{tt}+\displaystyle\int_{0}^{t}g(t-s)\Delta u(s)ds+|u_{t}|^{m(x)-2}u_{t}=|u|^{p(x)-2}u.$$This paper extends some of the results obtained by the authors and it is focused on new results which are consequence of the presence ofvariable exponents. 

scholarly journals A New Approach to Mannheim Curve in Euclidean 3-Space

2021 ◽  
Vol 54 ◽  
Author(s):  
Ali UÇUM ◽  
Çetin Camcı ◽  
Kazım İlarslan
Keyword(s):  
Euclidean Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Dimensional Euclidean Space ◽  
New Approach ◽  
3 Dimensional ◽  
Mannheim Curve ◽  
Necessary And Sufficient

In this article, a new approach is given for Mannheim curves in 3-dimensional Euclidean space. Thanks to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Mannheim curve in E³. In addition, related examples and graphs are given by showing that there can be Mannheim curves in Salkowski or anti-Salkowski curves as well as giving Mannheim mate curves, which are not in literature. Finally, the Mannheim partner curves are characterized in E³.

scholarly journals Blow-up and energy decay for a class of wave equations with nonlocal Kirchhoff-type diffusion and weak damping

2021 ◽  
Author(s):  
Menglan Liao ◽  
Zhong Tan
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Initial Data ◽  
Dirichlet Boundary Condition ◽  
Wave Equations ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Kirchhoff Type ◽  
Weak Damping

The purpose of this paper is to study the following equation driven by a nonlocal integro-differential operator $\mathcal{L}_K$: \[u_{tt}+[u]_s^{2(\theta-1)}\mathcal{L}_Ku+a|u_t|^{m-1}u_t=b|u|^{p-1}u\] with homogeneous Dirichlet boundary condition and initial data, where $[u]^2_s$ is the Gagliardo seminorm, $a\geq 0,~b>0,~0

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