scholarly journals Nonlocal time-porous medium equation: Weak solutions and finite speed of propagation

2019 ◽  
Vol 24 (8) ◽  
pp. 4031-4053
Author(s):  
Jean-Daniel Djida ◽  
◽  
Juan J. Nieto ◽  
Iván Area ◽  
◽  
...  
Keyword(s):  
Porous Medium ◽  
Weak Solutions ◽  
Porous Medium Equation ◽  
Finite Speed Of Propagation ◽  
Finite Speed ◽  
Medium Equation ◽  
Speed Of Propagation

scholarly journals On the Solutions of a Porous Medium Equation with Exponent Variable

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Huashui Zhan
Keyword(s):  
Porous Medium ◽  
Weak Solutions ◽  
Boundary Value ◽  
Porous Medium Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Medium Equation ◽  
Special Cases ◽  
The Stability ◽  
Initial Boundary Value

The paper studies the initial-boundary value problem of a porous medium equation with exponent variable. How to deal with nonlinear term with the exponent variable is the main dedication of this paper. The existence of the weak solution is proved by the monotone convergent method. Moreover, according to the different boundary value conditions, the stability of weak solutions is studied. In some special cases, the stability of weak solutions can be proved without any boundary value condition.

scholarly journals Energy estimates and convergence of weak solutions of the porous medium equation

Nonlinearity ◽  
2021 ◽  
Vol 34 (11) ◽  
pp. 7872-7915
Author(s):  
R De Paula ◽  
P Gonçalves ◽  
A Neumann
Keyword(s):  
Porous Medium ◽  
Weak Solutions ◽  
Porous Medium Equation ◽  
Energy Estimates ◽  
Medium Equation
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