Global existence and blow-up of solutions to a singular Non-Newton polytropic filtration equation with critical and supercritical initial energy

Guangyu Xu; Jun Zhou

doi:10.3934/cpaa.2018086

Article Contents

2018, Volume 17, Issue 5: 1805-1820. Doi: 10.3934/cpaa.2018086

This issue Previous Article On the blow-up solutions for the fractional nonlinear Schrödinger equation with combined power-type nonlinearities Next Article A free boundary problem for the Fisher-KPP equation with a given moving boundary

Global existence and blow-up of solutions to a singular Non-Newton polytropic filtration equation with critical and supercritical initial energy

Guangyu Xu^1, and
Jun Zhou^1,2, ,

1.
School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China
2.
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

* Corresponding author
* Corresponding author

Received: May 31, 2017

Revised: August 31, 2017

Published: April 2018

This work is partially supported by the the Basic and Advanced Research Project of CQC-STC grant cstc2016jcyjA0018 and NSFC 11201380.

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Abstract

In this paper, we revisit the singular Non-Newton polytropic filtration equation, which was studied extensively in the recent years. However, all the studies are mostly concerned with subcritical initial energy, i.e., $E(u_0)<d$ , where $E(u_0)$ is the initial energy and $d$ is the mountain-pass level. The main purpose of this paper is to study the behaviors of the solution with $E(u_0)≥d$ by potential well method and some differential inequality techniques.

Keywords:

Non-Newton polytropic filtration equation,
global existence,
blow-up.

Mathematics Subject Classification: 35B33, 35K50, 35K55, 35K63.

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