Blow-up for a degenerate parabolic equation with a nonlocal source

2008 ◽  
Vol 201 (1-2) ◽  
pp. 250-259 ◽  
Author(s):  
Congming Peng ◽  
Zuodong Yang
Keyword(s):  
Parabolic Equation ◽  
Degenerate Parabolic Equation ◽  
Blow Up ◽  
Nonlocal Source ◽  
Degenerate Parabolic

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.

Single-point blow-up for a doubly degenerate parabolic equation with nonlinear source

2011 ◽  
Vol 141 (3) ◽  
pp. 641-654 ◽  
Author(s):  
Chunlai Mu ◽  
Rong Zeng
Keyword(s):  
Parabolic Equation ◽  
Positive Solution ◽  
Large Class ◽  
Degenerate Parabolic Equation ◽  
Blow Up ◽  
Single Point ◽  
Degenerate Equation ◽  
Nonlinear Source ◽  
Degenerate Parabolic ◽  
Image Position

This paper deals with the positive solution to the doubly degenerate equationwhere σ > 0, m > 1, β > m(1 + σ). We prove single-point blow-up for a large class of radial decreasing solutions. Furthermore, the upper and lower estimates of the blow-up solution near the single blow-up point are obtained.

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