Existence and nonexistence of patterns on Riemannian manifolds

DOI10.1016/j.jmaa.2011.08.060zbMath1245.58010OpenAlexW1970866242WikidataQ115346148 ScholiaQ115346148MaRDI QIDQ645367

Fabio Punzo, Catherine Bandle, Tesei, Alberto

Publication date: 15 November 2011

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.2011.08.060

zbMATH Keywords

eigenvalue problemsemilinear parabolic problemstable solutionssurfaces of revolutions

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Boundary value problems on manifolds (58J32) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Semilinear parabolic equations (35K58)

Related Items (17)

The Destabilizing Effect of Unbalanced Reaction as Diffusivity Decreases on Reaction-Diffusion Equations in Boundaryless Surfaces ⋮ Rigidity results in diffusion Markov triples ⋮ On the Stability of Solutions of Semilinear Elliptic Equations with Robin Boundary Conditions on Riemannian Manifolds ⋮ Reaction-Diffusion Problems on Time-Dependent Riemannian Manifolds: Stability of Periodic Solutions ⋮ Classification of stable solutions for boundary value problems with nonlinear boundary conditions on Riemannian manifolds with nonnegative Ricci curvature ⋮ Patterns with prescribed numbers of critical points on topological tori ⋮ Blow-up on metric graphs and Riemannian manifolds ⋮ Non-existence of patterns for a class of weighted degenerate operators ⋮ Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions ⋮ Symmetry properties of stable solutions of semilinear elliptic equations in unbounded domains ⋮ Non-existence of patterns and gradient estimates in semilinear elliptic equations with Neumann boundary conditions ⋮ Continuous maximal regularity on uniformly regular Riemannian manifolds ⋮ On well-posedness of the semilinear heat equation on the sphere ⋮ A construction of patterns with many critical points on topological tori ⋮ The roles of diffusivity and curvature in patterns on surfaces of revolution ⋮ Stability results for a reaction-diffusion problem with mixed boundary conditions and applications to some symmetric cases ⋮ Parabolic Equations on Uniformly Regular Riemannian Manifolds and Degenerate Initial Boundary Value Problems

Cites Work

• Stable solutions of elliptic equations on Riemannian manifolds
• On a semilinear diffusion equation on a Riemannian manifold and its stable equilibrium solutions
• A nonlinear parabolic equation with varying domain
• The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains
• Asymptotic behavior and stability of solutions of semilinear diffusion equations
• Geometric theory of semilinear parabolic equations
• Instability results for reaction-diffusion equations with Neumann boundary conditions
• Instability results for reaction diffusion equations over surfaces of revolutions
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• Stability of stationary distributions in a space-dependent population growth process
• Instability results for an elliptic equation on compact Riemannian manifolds with non-negative Ricci curvature
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Riemannian geometry

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