Maximum Principles for Degenerate Elliptic-Parabolic Equations with Venttsel"s Boundary Condition

1981 ◽  
Vol 263 (2) ◽  
pp. 377
Author(s):  
Kazuo Amano
Keyword(s):  
Boundary Condition ◽  
Parabolic Equations ◽  
Maximum Principles ◽  
Degenerate Elliptic

Complete blow-up for quasilinear degenerate parabolic equations

2000 ◽  
Vol 130 (4) ◽  
pp. 877-908 ◽  
Author(s):  
R. Suzuki
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equation ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Image Position

Non-negative post-blow-up solutions of the quasilinear degenerate parabolic equation in RN (or a bounded domain with Dirichlet boundary condition) are studied. Various sufficient conditions for complete blow-up of solutions are given.

scholarly journals Strong Maximum Principles for Anisotropic Elliptic and Parabolic Equations

2012 ◽  
Vol 12 (1) ◽  
Author(s):  
Jérôme Vétois
Keyword(s):  
Parabolic Equations ◽  
Maximum Principles ◽  
Nonnegative Solutions ◽  
Elliptic And Parabolic Equations

AbstractWe investigate vanishing properties of nonnegative solutions of anisotropic elliptic and parabolic equations. We describe the optimal vanishing sets, and we establish strong maximum principles.

Blow-Up of Solutions for a Class of Reaction-Diffusion Equations with a Gradient Term under Nonlinear Boundary Condition

2012 ◽  
Vol 67 (8-9) ◽  
pp. 479-482 ◽  
Author(s):  
Junping Zhao
Keyword(s):  
Boundary Condition ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Blow Up ◽  
Existence Theorems ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Maximum Principles ◽  
Gradient Term

The blow-up of solutions for a class of quasilinear reaction-diffusion equations with a gradient term ut = div(a(u)b(x)▽u)+ f (x;u; |▽u|2; t) under nonlinear boundary condition ¶u=¶n+g(u) = 0 are studied. By constructing a new auxiliary function and using Hopf’s maximum principles, we obtain the existence theorems of blow-up solutions, upper bound of blow-up time, and upper estimates of blow-up rate. Our result indicates that the blow-up time T* may depend on a(u), while being independent of g(u) and f .

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