Global existence and blow-up for a porous medium system with nonlocal boundary conditions and nonlocal sources

2013 ◽  
Vol 82 ◽  
pp. 115-126 ◽  
Author(s):  
Zhuan Ye ◽  
Xiaojing Xu
Keyword(s):  
Porous Medium ◽  
Global Existence ◽  
Boundary Conditions ◽  
Blow Up ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Nonlocal Sources ◽  
Medium System

scholarly journals Blow-Up Solution of a Porous Medium Equation with Nonlocal Boundary Conditions

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Porous Medium ◽  
Boundary Conditions ◽  
Blow Up ◽  
Dimensional Space ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Porous Medium Equation ◽  
Nonlocal Boundary Conditions ◽  
Medium Equation ◽  
Inequality Technique

In this paper, we devote to studying the blow-up phenomena for a porous medium equation under nonlocal boundary conditions. Based on auxiliary functions and differential inequality technique, we derive the sufficient conditions to guarantee the existence of blow-up solutions under different measures and obtain an upper bound for blow-up time. Moreover, we demonstrate the lower bounds for blow-up time under some appropriate measures in R3 and in the higher-dimensional space Rnn≥3, respectively. At last, two examples are given to illustrate the applications of main results.

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 .

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