Growing solutions of the fractional \(p\)-Laplacian equation in the fast diffusion range

DOI10.1016/j.na.2021.112575zbMath1476.35320arXiv2103.00552OpenAlexW3204904886MaRDI QIDQ2238796

Juan Luis Vazquez

Publication date: 2 November 2021

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.00552

zbMATH Keywords

extinction\(p\)-Laplacian operatorfractional operatorssolutions with growing data

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Fractional partial differential equations (35R11) Quasilinear parabolic equations with (p)-Laplacian (35K92) Self-similar solutions to PDEs (35C06)

Related Items (3)

On a new fractional Sobolev space with variable exponent on complete manifolds ⋮ Morse's theory and local linking for a fractional \((p_1 (\mathrm{x}.,), p_2 (\mathrm{x}.,))\): Laplacian problems on compact manifolds ⋮ Asymptotic behaviors for the compressible Euler system with nonlinear velocity alignment

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlocal diffusion and applications
• Fractional \(p\)-Laplacian evolution equations
• Optimal existence and uniqueness theory for the fractional heat equation
• Ten equivalent definitions of the fractional Laplace operator
• Multiple continuation beyond blow-up.
• A fractional porous medium equation
• Degenerate parabolic equations
• A Widder's type theorem for the heat equation with nonlocal diffusion
• Non-negative solutions of the evolution p-Laplacian equation. Initial traces and Cauchy problem when \(1<p<2\)
• Fundamental solutions and asymptotic behaviour for the p-Laplacian equations
• Local smoothing effects, positivity, and Harnack inequalities for the fast \(p\)-Laplacian equation
• Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations
• The problem of blow-up in nonlinear parabolic equations
• The fractional \(p\)-Laplacian evolution equation in \(\mathbb{R}^N\) in the sublinear case
• The evolution fractional p-Laplacian equation in \(\mathbb{R}^N\). Fundamental solution and asymptotic behaviour
• Local boundedness and Hölder continuity for the parabolic fractional \(p\)-Laplace equations
• On fractional \(p\)-Laplacian parabolic problem with general data
• Quantitative local and global a priori estimates for fractional nonlinear diffusion equations
• Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type
• Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
• Radial equivalence for the two basic nonlinear degenerate diffusion equations
• The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation
• L'intégrale de Riemann-Liouville et le problème de Cauchy
• A General Fractional Porous Medium Equation
• Nonlinear Diffusion with Fractional Laplacian Operators
• The Cauchy Problem for u t = Δu m When 0 < m < 1
• Continuation of blowup solutions of nonlinear heat equations in several space dimensions
• The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion
• Fractional thoughts
• An Extension Problem Related to the Fractional Laplacian
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
• Nonlocal equations in bounded domains: a survey

This page was built for publication: Growing solutions of the fractional \(p\)-Laplacian equation in the fast diffusion range