Dynamics in Dumbbell domains. I: Continuity of the set of equilibria

DOI10.1016/j.jde.2006.06.002zbMath1110.35028OpenAlexW2110735942MaRDI QIDQ858693

José M. Arrieta, German Lozada-Cruz, Alexandre Nolasco De Carvalho

Publication date: 11 January 2007

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

Full work available at URL: http://hdl.handle.net/11449/38533

zbMATH Keywords

continuityreaction-diffusion equationstationary solutionshomogeneous Neumann boundary conditionsDumbbell domains

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Singular perturbations in context of PDEs (35B25)

Related Items (46)

Abstract degenerate fractional differential inclusions in Banach spaces ⋮ Analytical solutions to fractional evolution equations with almost sectorial operators ⋮ Coupled local/nonlocal models in thin domains ⋮ Spectral stability of the Steklov problem ⋮ Topological structural stability of partial differential equations on projected spaces ⋮ Dynamics for the damped wave equations on time-dependent domains ⋮ Elliptic and parabolic problems in thin domains with doubly weak oscillatory boundary ⋮ Limiting behavior of dynamics for stochastic reaction-diffusion equations with additive noise on thin domains ⋮ Spectral stability results for higher-order operators under perturbations of the domain ⋮ Strong solution for singularly nonautonomous evolution equation with almost sectorial operators ⋮ Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains ⋮ Interaction of localized large diffusion and boundary conditions ⋮ On the eigenvalues of the biharmonic operator with Neumann boundary conditions on a thin set ⋮ Generalised norm resolvent convergence: comparison of different concepts ⋮ Rate of convergence for reaction-diffusion equations with nonlinear Neumann boundary conditions and \(\mathcal{C}^1\) variation of the domain ⋮ Dynamics of the non-autonomous stochastic p-Laplacian parabolic problems on unbounded thin domains ⋮ The Neumann problem in an irregular domain ⋮ Gromov-Hausdorff stability of global attractors for the 3D Navier-Stokes equations with damping ⋮ Gromov–Hausdorff stability of global attractors for 3D Brinkman–Forchheimer equations ⋮ Spectral stability of the curlcurl operator via uniform Gaffney inequalities on perturbed electromagnetic cavities ⋮ Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries ⋮ Abstract fractional Cauchy problems with almost sectorial operators ⋮ Minimal coexistence configurations for multispecies systems ⋮ Reaction-diffusion problem in a thin domain with oscillating boundary and varying order of thickness ⋮ RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS: THE CASE OF A LIPSCHITZ DEFORMATION ⋮ Estimates on the distance of inertial manifolds ⋮ Regular random attractors for non-autonomous stochastic evolution equations with time-varying delays on thin domains ⋮ Non-existence of patterns and gradient estimates in semilinear elliptic equations with Neumann boundary conditions ⋮ Gromov-Hausdorff stability of global attractors of reaction diffusion equations under perturbations of the domain ⋮ A NOTE ON RESOLVENT CONVERGENCE ON A THIN DOMAIN ⋮ Asymptotic analysis of a semilinear elliptic equation in highly oscillating thin domains ⋮ Spectral stability for a class of fourth order Steklov problems under domain perturbations ⋮ Convergence estimates of the dynamics of a hyperbolic system with variable coefficients ⋮ Semilinear parabolic problems in thin domains with a highly oscillatory boundary ⋮ Higher order elliptic operators on variable domains. Stability results and boundary oscillations for intermediate problems ⋮ Distance of attractors of reaction-diffusion equations in thin domains ⋮ Persistence of the bifurcation structure for a semilinear elliptic problem on thin domains ⋮ Dynamics of parabolic equations via the finite element method. I: Continuity of the set of equilibria. ⋮ Asymptotic behaviour of the Steklov spectrum on dumbbell domains ⋮ Some estimates for resolvent operators under the discretization by finite element method ⋮ Dynamics in dumbbell domains. II: The limiting problem ⋮ Dynamics in dumbbell domains III. Continuity of attractors ⋮ Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions ⋮ Asymptotic properties in non-autonomous stochastic parabolic problems dominated by \(p\)-Laplacian operator on thin domains ⋮ Geometrically induced phase transitions in two-dimensional dumbbell-shaped domains ⋮ Parabolic problems in highly oscillating thin domains

Cites Work

• Lower semicontinuity of attractors of gradient systems and applications
• The singularly perturbed domain and the characterization for the eigenfunctions with Neumann boundary condition
• Dynamics in dumbbell domains III. Continuity of attractors
• Semigroups of linear operators and applications to partial differential equations
• A nonlinear parabolic equation with varying domain
• The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains
• Singular perturbation of domains and the semilinear elliptic equation. II
• Asymptotic behavior and stability of solutions of semilinear diffusion equations
• Geometric theory of semilinear parabolic equations
• Bifurcations caused by perturbing the domain in an elliptic equation
• Ordinary differential equations (ODE's) on inertial manifolds for reaction-diffusion systems in a singularly perturbed domain with several thin channels
• Instability results for reaction-diffusion equations with Neumann boundary conditions
• Stability of local minima and stable nonconstant equilibria
• Perturbation formula of eigenvalues in singularly perturbed domain
• Spectral convergence and nonlinear dynamics of reaction-diffusion equations under perturbations of the domain
• Neumann eigenvalue problems on exterior perturbations of the domain
• Reaction-diffusion equation on thin domains
• Reaction-diffusion systems on domains with thin channels
• On equilibrium solutions of diffusion equations with nonlinear boundary conditions
• Linear and quasilinear elliptic equations
• A functional-analytic framework for the study of elliptic equations on variable domains
• A General Approximation Scheme for Attractors of Abstract Parabolic Problems
• Approximative methods for nonlinear equations (two approaches to the convergence problem)
• Asymptotic Analysis of a Multidimensional Vibrating Structure
• Rates of Eigenvalues on a Dumbbell Domain. Simple Eigenvalue Case
• Attractors of parabolic problems with nonlinear boundary conditions. uniform bounds
• On the eigenvalues of a “dumb-bell with a thin handle”
• The effect of domain squeezing upon the dynamics of reaction-diffusion equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Dynamics in Dumbbell domains. I: Continuity of the set of equilibria