scholarly journals A very singular solution for the slow diffusion equation with nonlinear convection

2008 ◽  
Vol 337 (2) ◽  
pp. 1211-1225 ◽  
Author(s):  
Zhong Bo Fang ◽  
Minkyu Kwak
Keyword(s):  
Diffusion Equation ◽  
Singular Solution ◽  
Nonlinear Convection ◽  
Slow Diffusion ◽  
Very Singular Solution ◽  
Slow Diffusion Equation

scholarly journals Lower Bounds Estimate for the Blow-Up Time of a Slow Diffusion Equation with Nonlocal Source and Inner Absorption

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Zhong Bo Fang ◽  
Rui Yang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Lower Bounds ◽  
Blow Up ◽  
Neumann Boundary ◽  
Nonlocal Source ◽  
Slow Diffusion ◽  
Homogeneous Neumann Boundary Condition ◽  
Inner Absorption ◽  
Slow Diffusion Equation

We investigate a slow diffusion equation with nonlocal source and inner absorption subject to homogeneous Dirichlet boundary condition or homogeneous Neumann boundary condition. Based on an auxiliary function method and a differential inequality technique, lower bounds for the blow-up time are given if the blow-up occurs in finite time.

scholarly journals Global null controllability of the 1-dimensional nonlinear slow diffusion equation

2013 ◽  
Vol 34 (3) ◽  
pp. 333-344 ◽  
Author(s):  
Jean-Michel Coron ◽  
Jesús Ildefonso Díaz ◽  
Abdelmalek Drici ◽  
Tommaso Mingazzini
Keyword(s):  
Diffusion Equation ◽  
Null Controllability ◽  
Slow Diffusion ◽  
Slow Diffusion Equation
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