scholarly journals Quenching Rate for the Porous Medium Equation with a Singular Boundary Condition

2011 ◽  
Vol 02 (09) ◽  
pp. 1134-1139
Author(s):  
Zhengce Zhang ◽  
Yanyan Li
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Porous Medium Equation ◽  
Singular Boundary ◽  
Quenching Rate ◽  
Medium Equation ◽  
Singular Boundary 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 .

scholarly journals Quenching for a Non-Newtonian Filtration Equation with a Singular Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Xiliu Li ◽  
Chunlai Mu ◽  
Qingna Zhang ◽  
Shouming Zhou
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Finite Time ◽  
Singular Boundary ◽  
Quenching Rate ◽  
Filtration Equation ◽  
Laplacian Equation ◽  
Singular Boundary Condition

This paper deals with a nonlinearp-Laplacian equation with singular boundary conditions. Under proper conditions, the solution of this equation quenches in finite time and the only quenching point thatisx=1are obtained. Moreover, the quenching rate of this equation is established. Finally, we give an example of an application of our results.

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