On well-posedness of semilinear parabolic and elliptic problems in the hyperbolic space

DOI10.1016/j.jde.2011.05.033zbMath1241.35124OpenAlexW1989258415MaRDI QIDQ639507

Fabio Punzo

Publication date: 22 September 2011

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

Full work available at URL: https://doi.org/10.1016/j.jde.2011.05.033

zbMATH Keywords

Laplace-Beltrami operatorsingular solutionssemigroup theorynonuniqueness of weak solutions

Mathematics Subject Classification ID

Weak solutions to PDEs (35D30) Semilinear elliptic equations (35J61) Semilinear parabolic equations (35K58) Positive solutions to PDEs (35B09) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (12)

Solvability of a semilinear heat equation on Riemannian manifolds ⋮ On nonlinear Schrödinger equations on the hyperbolic space ⋮ On the nonlinear Schrödinger equation on the Poincaré ball model ⋮ A critical exponent of Joseph-lundgren type for an Hénon equation on the hyperbolic space ⋮ On well-posedness of the semilinear heat equation on the sphere ⋮ Unnamed Item ⋮ Parabolic Equations on Uniformly Regular Riemannian Manifolds and Degenerate Initial Boundary Value Problems ⋮ Porous medium equations on manifolds with critical negative curvature: unbounded initial data ⋮ Kirchhoff-type problems on a geodesic ball of the hyperbolic space ⋮ Separation phenomena of radial solutions to the Lane-Emden equation on non-compact Riemannian manifolds ⋮ Blow-up of radially symmetric solutions for a semilinear heat equation on hyperbolic space ⋮ Classification of radial solutions to Hénon type equation on the hyperbolic space

Cites Work

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• The Fujita exponent for the Cauchy problem in the hyperbolic space
• \(L^p\) spectral theory and heat dynamics of locally symmetric spaces
• Symmetry and related properties via the maximum principle
• Lectures on hyperbolic geometry
• Serrin's result for hyperbolic space and sphere
• Non-unicité des solutions d'une équation d'évolution non-linéaire
• Singular Behavior in Nonlinear Parabolic Equations
• Uniqueness and nonuniqueness for positive radial solutions of Δu + f(u, r) = 0
• The Heat Kernel on Hyperbolic Space
• Uniqueness of Radial Solutions of Semilinear Elliptic Equations
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds

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