Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains
From MaRDI portal
Publication:1867238
DOI10.1016/S0022-0396(02)00014-1zbMath1024.35046OpenAlexW2058145942MaRDI QIDQ1867238
Frédérique Simondon, Peter Poláčik
Publication date: 2 April 2003
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0022-0396(02)00014-1
Reaction-diffusion equations (35K57) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10)
Related Items (25)
Global dynamics of a nonlocal non-uniformly parabolic equation arising from the curvature flow* ⋮ Convergence to equilibrium for the Cahn-Hilliard equation with dynamic boundary conditions ⋮ Stability analysis of asymptotic profiles for sign-changing solutions to fast diffusion equations ⋮ A note on parabolic equation with nonlinear dynamical boundary condition ⋮ On a system of coupled Cahn-Hilliard equations ⋮ Asymptotic behavior of a nonisothermal viscous Cahn-Hilliard equation with inertial term ⋮ Existence, multiplicity, shape and attractivity of heterogeneous steady states for bistable reaction-diffusion equations in the plane ⋮ Global existence and finite time blow-up for the \(m\)-Laplacian parabolic problem ⋮ Spatially monotone homoclinic orbits in nonlinear parabolic equations of super-fast diffusion type ⋮ Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation ⋮ Oscillating solutions and large \(\omega\)-limit sets in a degenerate parabolic equation ⋮ Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction ⋮ Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations ⋮ A review on the Cahn-Hilliard equation: classical results and recent advances in dynamic boundary conditions ⋮ Uniqueness of limit flow for a class of quasi-linear parabolic equations ⋮ On the convergence to stationary solutions for a semilinear wave equation with an acoustic boundary condition ⋮ Convergence to equilibrium for a parabolic-hyperbolic phase-field system with dynamical boundary condition ⋮ Non-genericity of initial data with punctual \(\omega \)-limit set ⋮ Gradient stability of high-order BDF methods and some applications ⋮ Analysis of the Cahn–Hilliard Equation with a Chemical Potential Dependent Mobility ⋮ Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation ⋮ Convergence to equilibrium for a second-order time semi-discretization of the Cahn-Hilliard equation ⋮ Convergence to equilibrium for the damped semilinear wave equation with critical exponent and dissipative boundary condition ⋮ Control of reaction-diffusion models in biology and social sciences ⋮ CONVERGENCE TO EQUILIBRIUM FOR A PARABOLIC–HYPERBOLIC PHASE-FIELD SYSTEM WITH NEUMANN BOUNDARY CONDITIONS
Cites Work
- Invariant manifolds for flows in Banach spaces
- The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension
- Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
- A reduction principle for nonautonomous systems in infinite-dimensional spaces
- Geometric theory of semilinear parabolic equations
- Structure of the set of steady-state solutions and asymptotic behavior of semilinear heat equations
- Smooth invariant foliations in infinite dimensional spaces
- Convergence in gradient-like systems with applications to PDE
- Manifolds, tensor analysis, and applications.
- Convergence of solutions of one-dimensional semilinear parabolic equations
- Invariant foliations for \(C^1\) semigroups in Banach spaces
- A simple unified approach to some convergence theorems of L. Simon
- Inverse problems and chaotic dynamics of parabolic equations on arbitrary spatial domains
- Nonconvergent bounded trajectories in semilinear heat equations
- An abstract approach to smoothness of invariant manifolds
- Generic properties of nonlinear boundary value problems
- Perturbation of elliptic operators and complex dynamics of parabolic partial differential equations
- Analytic semigroups and optimal regularity in parabolic problems
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains