The fractional porous medium equation on the hyperbolic space

DOI10.1007/s00526-020-01817-2zbMath1448.35540arXiv2003.01449OpenAlexW3085986463WikidataQ114229038 ScholiaQ114229038MaRDI QIDQ2204088

Gabriele Grillo, Matteo Bonforte, Debdip Ganguly, Elvise Berchio

Publication date: 2 October 2020

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.01449

zbMATH Keywords

fractional Green's functionfractional Laplacian

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for second-order parabolic equations (35K15) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Fractional partial differential equations (35R11) Quasilinear parabolic equations (35K59) PDEs on manifolds (35R01)

Related Items (4)

Functional inequalities involving nonlocal operators on complete Riemannian manifolds and their applications to the fractional porous medium equation ⋮ Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities ⋮ The Cauchy-Dirichlet problem for singular nonlocal diffusions on bounded domains ⋮ Three representations of the fractional \(p\)-Laplacian: semigroup, extension and Balakrishnan formulas

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains
• Fundamental solution and long time behavior of the porous medium equation in hyperbolic space
• A priori estimates for fractional nonlinear degenerate diffusion equations on bounded domains
• A fractional porous medium equation
• Some constructions for the fractional Laplacian on noncompact manifolds
• Fractional porous media equations: existence and uniqueness of weak solutions with measure data
• Smoothing effects for the porous medium equation on Cartan-Hadamard manifolds
• Fractional nonlinear degenerate diffusion equations on bounded domains. I: Existence, uniqueness and upper bounds.
• Continuity of the temperature in boundary heat control problems
• Regularizing effects for \(u_ t\) + A phi(u) = 0 in \(L^ 1\).
• Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains
• The porous medium equation on Riemannian manifolds with negative curvature: the superquadratic case
• The porous medium equation with large initial data on negatively curved Riemannian manifolds
• Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space
• The porous medium equation with measure data on negatively curved Riemannian manifolds
• Nonlinear characterizations of stochastic completeness
• Regularity of Lagrangian flows over \(\operatorname{RCD}^*(K, N)\) spaces
• Classical solutions and higher regularity for nonlinear fractional diffusion equations
• Fast diffusion flow on manifolds of nonpositive curvature
• Quantitative local and global a priori estimates for fractional nonlinear diffusion equations
• Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
• Nonlinear semigroups in Hilbert space
• Existence and maximalL^p-regularity of solutions for the porous medium equation on manifolds with conical singularities
• A General Fractional Porous Medium Equation
• Radial fast diffusion on the hyperbolic space
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Fractional Laplacians and extension problems: The higher rank case
• A nonlocal diffusion problem on manifolds
• Smoothness and long time existence for solutions of the porous medium equation on manifolds with conical singularities
• Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains
• An Extension Problem Related to the Fractional Laplacian
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces

This page was built for publication: The fractional porous medium equation on the hyperbolic space