On fractional \(p\)-Laplacian parabolic problem with general data
type: Item
instance of: scholarly article
title: On fractional \(p\)-Laplacian parabolic problem with general data
zbMATH Open document ID: 1392.35184
author: Ahmed Attar
author: Boumediene Abdellaoui
author: Rachid Bentifour
author: Ireneo Peral
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2018-04-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1612.01301
review text: The authors prove the existence of a weak solution that belongs to a suitable fractional Sobolev space for the considered problem \[ \begin{cases} u_t+(-\Delta^s_p)u=f(x,t)&\text{in }\Omega_T\equiv\Omega\times(0,T),\\ u=0&\text{in }(\mathbb R^N\setminus\Omega)\times(0,T),\\ u(x,0)=u(x)&\text{in }\Omega, \end{cases} \tag{P} \] in the case of \(p\neq 2\), by using the way limit of approximations. Moreover, if the data \((f,u_0)\) are nonnegative then they obtained the weak solution of problem (P) as an entropy nonnegative solution. Finally they also showed extinction in the finite time, nonfinite speed of propogation and extinction for concave case to the considered problem according the values of \(p\).
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K92
Mathematics Subject Classification ID: 35B09
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6857764
zbMATH Keywords: nonlinear nonlocal parabolic problems
zbMATH Keywords: entropy solution
zbMATH Keywords: finite time extinction
zbMATH Keywords: speed of propagation
reviewed by: Fatma Gamze Duzgun
MaRDI profile type: Publication
OpenAlex ID: W2560445528
arXiv ID: 1612.01301
cites work: On the fractional \(p\)-Laplacian equations with weight and general datum
cites work: Optimal results for the fractional heat equation involving the Hardy potential
cites work: Some remarks on quasilinear parabolic problems with singular potential and a reaction term
cites work: Q4073917
cites work: Global Behavior of the Cauchy Problem for Some Critical Nonlinear Parabolic Equations
cites work: Renormalised solutions of nonlinear parabolic problems with L1 data: existence and uniqueness
cites work: Existence and uniqueness of a renormalized solution for a fairly general class of nonlinear parabolic problems
cites work: Approximated solutions of equations with \(L^ 1\) data. Application to the \(H\)-convergence of quasilinear parabolic equations
cites work: Nonlocal Harnack inequalities
cites work: Hitchhiker's guide to the fractional Sobolev spaces
cites work: Radial fractional Laplace operators and Hessian inequalities
cites work: Classical Fourier Analysis
cites work: Nonlocal equations with measure data
cites work: Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations
cites work: Q5890172
cites work: Fractional \(p\)-Laplacian evolution equations
cites work: Optimal reaction exponent for some qualitative properties of solutions to the \(p\)-heat equation
cites work: Elliptic PDEs, measures and capacities. From the Poisson equation to nonlinear Thomas-Fermi problems
cites work: Existence and uniqueness of “entropy” solutions of parabolic problems with L1 data
cites work: The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation
DOI: 10.1007/S10231-017-0682-Z
description: scientific article