On time decay estimates for solutions of the second mixed problem for a quasilinear parabolic equation

2009 ◽  
Vol 160 (3) ◽  
pp. 308-318
Author(s):  
O. M. Botsenyuk
Keyword(s):  
Parabolic Equation ◽  
Mixed Problem ◽  
Quasilinear Parabolic Equation ◽  
Decay Estimates ◽  
Time Decay ◽  
Quasilinear Parabolic

scholarly journals Extinction Phenomenon and Decay Estimate for a Quasilinear Parabolic Equation with a Nonlinear Source

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Dengming Liu ◽  
Luo Yang
Keyword(s):  
Parabolic Equation ◽  
Decay Estimate ◽  
Energy Estimate ◽  
Quasilinear Parabolic Equation ◽  
Upper And Lower Solutions ◽  
Decay Estimates ◽  
Nonlinear Source ◽  
Quasilinear Parabolic

By energy estimate approach and the method of upper and lower solutions, we give the conditions on the occurrence of the extinction and nonextinction behaviors of the solutions for a quasilinear parabolic equation with nonlinear source. Moreover, the decay estimates of the solutions are studied.

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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