On the existence with exponential decay and the blow-up of solutions for coupled systems of semi-linear corner-degenerate parabolic equations with singular potentials

2020 ◽  
Vol 41 (1) ◽  
pp. 257-282
Author(s):  
Hua Chen ◽  
Nian Liu
Keyword(s):  
Exponential Decay ◽  
Parabolic Equations ◽  
Blow Up ◽  
Coupled Systems ◽  
Degenerate Parabolic Equations ◽  
Singular Potentials ◽  
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.

Localized Blow-Up Regimes for Quasilinear Doubly Degenerate Parabolic Equations

2019 ◽  
Vol 106 (3-4) ◽  
pp. 639-650 ◽  
Author(s):  
A. E. Shishkov ◽  
Ye. A. Yevgenieva
Keyword(s):  
Parabolic Equations ◽  
Blow Up ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic

scholarly journals Asymptotic Properties of Solutions to the Cauchy Problem for Degenerate Parabolic Equations with Inhomogeneous Density on Manifolds

2021 ◽  
Author(s):  
Daniele Andreucci ◽  
Anatoli F. Tedeev
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equations ◽  
Blow Up ◽  
Asymptotic Properties ◽  
Degenerate Parabolic Equations ◽  
Isoperimetric Function ◽  
Finite Speed Of Propagation ◽  
The Cauchy Problem ◽  
Inhomogeneous Density ◽  
Degenerate Parabolic

AbstractWe consider the Cauchy problem for doubly nonlinear degenerate parabolic equations with inhomogeneous density on noncompact Riemannian manifolds. We give a qualitative classification of the behavior of the solutions of the problem depending on the behavior of the density function at infinity and the geometry of the manifold, which is described in terms of its isoperimetric function. We establish for the solutions properties as: stabilization of the solution to zero for large times, finite speed of propagation, universal bounds of the solution, blow up of the interface. Each one of these behaviors of course takes place in a suitable range of parameters, whose definition involves a universal geometrical characteristic function, depending both on the geometry of the manifold and on the asymptotics of the density at infinity.

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