The local and global existence of solutions for a time fractional complex Ginzburg-Landau equation

DOI10.1016/j.jmaa.2018.08.008zbMath1404.35426OpenAlexW2887438190MaRDI QIDQ1798980

Menglong Su, Quan-Guo Zhang, Ya-Ning Li

Publication date: 18 October 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2018.08.008

zbMATH Keywords

Cauchy problemglobal existencetime fractional Ginzburg-Landau equation

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11) Ginzburg-Landau equations (35Q56)

Related Items

Regularity results of solution uniform in time for complex Ginzburg-Landau equation, On the blow-up of solutions for a fractional diffusion equation with nonlinear memory and reaction terms in a bounded domain, Convergence and superconvergence analysis of finite element methods for nonlinear Ginzburg-Landau equation with Caputo derivative, Solvability for time‐fractional semilinear parabolic equations with singular initial data, Global existence and blow-up of solutions of the Cauchy problem for a time fractional diffusion system, EXISTENCE AND NON-EXISTENCE OF GLOBAL SOLUTIONS FOR THE SEMILINEAR COMPLEX GINZBURG-LANDAU TYPE EQUATION IN HOMOGENEOUS AND ISOTROPIC SPACETIME

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stochastic solution of fractional Fokker-Planck equations with space-time-dependent coefficients
• A parabolic problem with a fractional time derivative
• Fundamental solutions of the time fractional diffusion-wave and parabolic Dirac operators
• The nonexistence of global solutions for a time fractional nonlinear Schrödinger equation without gauge invariance
• Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives
• The blow-up and global existence of solutions of Cauchy problems for a time fractional diffusion equation
• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• Abstract fractional Cauchy problems with almost sectorial operators
• Nonlocal Cauchy problem for fractional evolution equations
• On fractional powers of generators of fractional resolvent families
• Blow-up profile for the complex Ginzburg-Landau equation
• Semigroups of linear operators and applications to partial differential equations
• The Cauchy problem in local spaces for the complex Ginzburg-Landau equation. II: Contraction methods
• Global existence and smoothing effect for the complex Ginzburg-Landau equation with \(p\)-Laplacian
• Cauchy problem for fractional diffusion equations
• The Cauchy problem in local spaces for the complex Ginzburg-Landau equation. I: Compactness methods
• Fractional Schrödinger equations with potential and optimal controls
• A De Giorgi-Nash type theorem for time fractional diffusion equations
• The cubic complex Ginzburg-Landau equation for a backward bifurcation
• Time fractional Schrödinger equation revisited
• Finite-time blowup for a complex Ginzburg-Landau equation with linear driving
• Some generalized fractional calculus operators and their applications in integral equations
• Mild solutions to the time fractional Navier-Stokes equations in \(\mathbb{R}^N\)
• Existence and uniqueness for parabolic problems with Caputo time derivative
• Well-posedness and regularity of the Cauchy problem for nonlinear fractional in time and space equations
• Time fractional Schrödinger equation
• Finite-Time Blowup for a Complex Ginzburg--Landau Equation
• Analytic semigroups and optimal regularity in parabolic problems