scholarly journals Global Existence and Extinction Singularity for a Fast Diffusive Polytropic Filtration Equation with Variable Coefficient

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Dengming Liu ◽  
Changyu Liu
Keyword(s):  
Weak Solution ◽  
Global Existence ◽  
Sobolev Inequality ◽  
Variable Coefficient ◽  
Existence Result ◽  
Energy Estimate ◽  
Differential Inequalities ◽  
Filtration Equation ◽  
Global Existence Result

In this article, we deal with an inhomogeneous fast diffusive polytropic filtration equation. By using the energy estimate approach, Hardy–Littlewood–Sobolev inequality, and a series of ordinary differential inequalities, we prove the global existence result and obtain the conditions on the occurrence of the extinction phenomenon of the weak solution.

scholarly journals Extinction behavior for a parabolic $ p $-Laplacian equation with gradient source and singular potential

2021 ◽  
Vol 7 (1) ◽  
pp. 915-924
Author(s):  
Dengming Liu ◽  
◽  
Luo Yang
Keyword(s):  
Weak Solution ◽  
Sobolev Inequality ◽  
Singular Potential ◽  
Energy Estimate ◽  
Differential Inequalities ◽  
Laplacian Equation ◽  
Solution Methods

<abstract><p>We concern with the extinction behavior of the solution for a parabolic $ p $-Laplacian equation with gradient source and singular potential. By energy estimate approach, Hardy-Littlewood-Sobolev inequality, a series of ordinary differential inequalities, and super-solution and sub-solution methods, we obtain the conditions on the occurrence of the extinction phenomenon of the weak solution.</p></abstract>

Global Existence for the Two-Dimensional Euler Equations in a Critical Besov Space

2011 ◽  
Vol 271-273 ◽  
pp. 791-796
Author(s):  
Kun Qu ◽  
Yue Zhang
Keyword(s):  
Global Existence ◽  
Transport Equation ◽  
Besov Space ◽  
Euler Equations ◽  
Existence Result ◽  
Two Dimensional ◽  
Critical Besov Space ◽  
Global Existence Result

In this paper we prove the global existence for the two-dimensional Euler equations in the critical Besov space. Making use of a new estimate of transport equation and Littlewood-Paley theory, we get the global existence result.

On a critical nonlinear problem involving the fractional Laplacian

2021 ◽  
pp. 2150066
Author(s):  
Azeb Alghanemi ◽  
Hichem Chtioui
Keyword(s):  
Global Existence ◽  
Bounded Domain ◽  
Nonlinear Problem ◽  
Fractional Laplacian ◽  
Existence Result ◽  
Counting Formula ◽  
Global Existence Result

Fractional Yamabe-type equations of the form [Formula: see text] in [Formula: see text] on [Formula: see text], where [Formula: see text] is a bounded domain of [Formula: see text], [Formula: see text] is a given function on [Formula: see text] and [Formula: see text], is the fractional Laplacian are considered. Bahri’s estimates in the fractional setting will be proved and used to establish a global existence result through an index-counting formula.

A Global Existence Result for Korteweg System in the Critical LP Framework

2019 ◽  
Vol 39 (6) ◽  
pp. 1639-1660
Author(s):  
Zhensheng Gao ◽  
Yan Liang ◽  
Zhong Tan
Keyword(s):  
Global Existence ◽  
Existence Result ◽  
Global Existence Result

Global Existence Result for the Generalized Peterlin Viscoelastic Model

2017 ◽  
Vol 49 (4) ◽  
pp. 2950-2964 ◽  
Author(s):  
Mária Lukáčová-Medviďová ◽  
Hana Mizerová ◽  
Šárka Nečasová ◽  
Michael Renardy
Keyword(s):  
Global Existence ◽  
Existence Result ◽  
Viscoelastic Model ◽  
Global Existence Result
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