Global and blowup solutions of quasilinear parabolic equation with critical Sobolev exponent and lower energy initial value

2001 ◽  
Vol 2001 (1) ◽  
pp. 245838 ◽  
Author(s):  
Zhong Tan ◽  
Zheng-An Yao
Keyword(s):  
Parabolic Equation ◽  
Lower Energy ◽  
Quasilinear Parabolic Equation ◽  
Critical Sobolev Exponent ◽  
Initial Value ◽  
Sobolev Exponent ◽  
Quasilinear Parabolic

scholarly journals Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Bo Fang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Quasilinear Parabolic Equation ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Blow Up Analysis ◽  
Inner Absorption ◽  
Quasilinear Parabolic

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee thatu(x,t)exists globally or blows up at some finite timet*. Moreover, an upper bound fort*is derived. Under somewhat more restrictive conditions, a lower bound fort*is also obtained.

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