On the explicit construction of an ODE which has the same dynamics as a scalar parabolic PDE

DOI10.1016/0022-0396(87)90104-5zbMath0634.35037OpenAlexW2014667228MaRDI QIDQ1096786

Giorgio Fusco

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0022-0396(87)90104-5

zbMATH Keywords

ordinary differential equationsstructural stabilityglobal attractorinvariant manifoldinfinite dimensional dynamical systemscalar parabolic equationlimit singular function

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Initial value problems for second-order parabolic equations (35K15) Dynamical systems and ergodic theory (37-XX)

Related Items (13)

Diffusive coupling, dissipation, and synchronization ⋮ Reaction-diffusion problems in cell tissues ⋮ Dynamics of interfaces in a scalar parabolic equation with variable diffusion coefficients ⋮ Rate of convergence of attractors for singularly perturbed semilinear problems ⋮ Delay-partial differential equations with some large diffusion ⋮ Convergence of nonautonomous multivalued problems with large diffusion to ordinary differential inclusions ⋮ Parabolic equations with localized large diffusion: rate of convergence of attractors ⋮ Contracting sets and dissipation ⋮ On spectral convergence for some parabolic problems with locally large diffusion ⋮ Large time dynamics of a nonlinear spring-mass-damper model ⋮ Persistence of the bifurcation structure for a semilinear elliptic problem on thin domains ⋮ A Morse-Smale ordinary differential equation in \(\mathbb{R}^N\) ⋮ Conley index continuation for a singularly perturbed periodic boundary value problem

Cites Work

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• Generic properties of stationary state solutions of reaction-diffusion equations
• Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations
• Large diffusivity and asymptotic behavior in parabolic systems
• Asymptotic behavior and stability of solutions of semilinear diffusion equations
• Geometric theory of semilinear parabolic equations
• Stability of Morse-Smale maps
• Stable equilibria with variable diffusion
• Stable Equilibria in a Scalar Parabolic Equation with Variable Diffusion
• Generic properties of equilibria of reaction-diffusion equations with variable diffusion

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