scholarly journals Roles of Weight Functions to a Nonlocal Porous Medium Equation with Inner Absorption and Nonlocal Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhong Bo Fang ◽  
Jianyun Zhang ◽  
Su-Cheol Yi
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Blow Up ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Porous Medium Equation ◽  
Weight Functions ◽  
Medium Equation ◽  
Nonnegative Solutions ◽  
Inner Absorption

This work is concerned with an initial boundary value problem for a nonlocal porous medium equation with inner absorption and weighted nonlocal boundary condition. We obtain the roles of weight function on whether determining the blowup of nonnegative solutions or not and establish the precise blow-up rate estimates under some suitable condition.

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 .

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

2013 ◽  
Vol 634-638 ◽  
pp. 3954-3957
Author(s):  
Lin Zhao ◽  
Yun Zhu Gao
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Blow Up ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Porous Medium Equation ◽  
Localized Source ◽  
Medium Equation

In this paper, a porous medium equation with nonlocal boundary condition and a localized source is considered. The existence and blow-up properties of solutions are obtained under some conditions.

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