scholarly journals Porous medium equation with a blow-up nonlinearity and a non-decreasing constraint

2019 ◽  
Vol 26 (2) ◽  
Author(s):  
Goro Akagi ◽  
Stefano Melchionna
Keyword(s):  
Porous Medium ◽  
Blow Up ◽  
Porous Medium Equation ◽  
Medium Equation

Global Existence and Blow-Up of Solutions for a Porous Medium Equation

2012 ◽  
Vol 461 ◽  
pp. 532-536
Author(s):  
Yun Zhu Gao ◽  
Xi Meng ◽  
Hong Gai
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Global Existence ◽  
Blow Up ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Porous Medium Equation ◽  
Local Source ◽  
Medium Equation ◽  
The Fixed Point Theorem

In this paper, a porous medium equation with local source and nonlocal boundary condition is studied. By using the fixed point theorem and comparison principle. The global existence and blow-up of solutions are obtained .

scholarly journals Singularity Analysis for a Class of Porous Medium Equation with Time-Dependent Coefficients

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Anyin Xia ◽  
Xianxiang Pu ◽  
Shan Li
Keyword(s):  
Porous Medium ◽  
Global Regularity ◽  
Blow Up ◽  
Porous Medium Equation ◽  
Singularity Analysis ◽  
Dirichlet Boundary Conditions ◽  
Time Dependent ◽  
Medium Equation ◽  
Regularity Results ◽  
Homogeneous Dirichlet Boundary Conditions

This paper concerns the singularity and global regularity for the porous medium equation with time-dependent coefficients under homogeneous Dirichlet boundary conditions. Firstly, some global regularity results are established. Furthermore, we investigate the blow-up solution to the boundary value problem. The upper and lower estimates to the lifespan of the singular solution are also obtained here.

Instant blow-up solutions for porous medium equation with sources

2014 ◽  
Vol 8 ◽  
pp. 4853-4858
Author(s):  
Huiling Duan ◽  
Tao Peng ◽  
Liangwei Wang
Keyword(s):  
Porous Medium ◽  
Blow Up ◽  
Porous Medium Equation ◽  
Medium Equation
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