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.

scholarly journals On some degenerate parabolic equations II

1973 ◽  
Vol 52 ◽  
pp. 61-84 ◽  
Author(s):  
Tadato Matsuzawa
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equation ◽  
Pseudodifferential Operators ◽  
Degenerate Parabolic Equations ◽  
Smooth Functions ◽  
Fundamental Assumption ◽  
Degenerate Parabolic ◽  
The Given ◽  
Complex Valued

In the article I: [8], we have proved the hypoellipticity of a degenerate parabolic equation of the form:where the coefficients a(x, t), b(x,t) and c(x, t) are complex valued smooth functions. The fundamental assumption on the coefficients is that Re a(x, t) satisfies the condition of Nirenberg and Treves ([8], (1.5)). To prove the hypoellipticity we have constructed recurcively the parametrices as pseudodifferential operators with parameter. This method may be viewed as an improvement of that of [9] and [7]. We have analyzed the properties of these parametrices by estimating the symbols with parameter associated with the given operator. We shall summerize these results in §3.

scholarly journals Hölder gradient estimates for a class of singular or degenerate parabolic equations

2017 ◽  
Vol 8 (1) ◽  
pp. 845-867 ◽  
Author(s):  
Cyril Imbert ◽  
Tianling Jin ◽  
Luis Silvestre
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equation ◽  
Divergence Form ◽  
Gradient Estimates ◽  
Degenerate Parabolic Equations ◽  
Spatial Gradients ◽  
Degenerate Parabolic ◽  
Laplacian Equations ◽  
Hölder Estimates

Abstract We prove interior Hölder estimates for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic equation u_{t}=\lvert\nabla u\rvert^{\kappa}\operatorname{div}(\lvert\nabla u\rvert^{p-% 2}\nabla u), where {p\in(1,\infty)} and {\kappa\in(1-p,\infty)} . This includes the from {L^{\infty}} to {C^{1,\alpha}} regularity for parabolic p-Laplacian equations in both divergence form with {\kappa=0} , and non-divergence form with {\kappa=2-p} .

Sign in / Sign up

Export Citation Format

Share Document