Trivial stationary solutions to the Kuramoto-Sivashinsky and certain nonlinear elliptic equations

DOI10.1016/j.jde.2006.08.002zbMath1113.35008arXivmath/0603723OpenAlexW2085100977MaRDI QIDQ858702

Edriss S. Titi, Yan Ping Cao

Publication date: 11 January 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603723

zbMATH Keywords

Kuramoto-Sivashinsky equationnonexistence of nontrivial solutions

Mathematics Subject Classification ID

Related Items (9)

On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation ⋮ Regularity criteria for the Kuramoto-Sivashinsky equation in dimensions two and three ⋮ Gevrey regularity for a class of dissipative equations with applications to decay ⋮ Asymptotic behavior of solutions for the time-delayed Kuramoto-Sivashinsky equation ⋮ Existence and nonexistence of a global solution to the Kuramoto-Sivashinsky equation ⋮ Application of \(G^\prime/G\)-expansion method to Kuramoto-Sivashinsky equation ⋮ Radial asymptotically periodic solutions of the Kuramoto-Sivashinsky equation ⋮ On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations ⋮ Long-time behavior of a two-layer model of baroclinic quasi-geostrophic turbulence

Cites Work

• Unnamed Item
• Unnamed Item
• Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension
• Elementary particles as solutions of the Sivashinsky equation
• Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations
• Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors
• Steady solutions of the Kuramoto-Sivashinsky equation
• Inertial manifolds for nonlinear evolutionary equations
• Infinite-dimensional dynamical systems in mechanics and physics
• Integral manifolds and inertial manifolds for dissipative partial differential equations
• Global analysis of the phase portrait for the Kuramoto-Sivashinsky equation
• A global attracting set for the Kuramoto-Sivashinsky equation
• Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions
• Determining nodes for the Kuramoto-Sivashinsky equation
• Back in the Saddle Again: A Computer Assisted Study of the Kuramoto–Sivashinsky Equation
• Uncertainty estimates andL₂bounds for the Kuramoto–Sivashinsky equation
• The Well-Posedness of the Kuramoto–Sivashinsky Equation
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• On Flame Propagation Under Conditions of Stoichiometry
• Local dissipativity and attractors for the Kuramoto-Sivashinsky equation in thin 2D domains
• Stability of the kuramoto‐sivashinsky and related systems
• Finite-time singularity versus global regularity for hyper-viscous Hamilton–Jacobi-like equations
• New bounds for the Kuramoto‐Sivashinsky equation
• On the non-homogeneous stationary Kuramoto-Sivashinsky equation

This page was built for publication: Trivial stationary solutions to the Kuramoto-Sivashinsky and certain nonlinear elliptic equations