scholarly journals On the viscosity solutions to a degenerate parabolic differential equation

2014 ◽  
Vol 194 (5) ◽  
pp. 1423-1454 ◽  
Author(s):  
Tilak Bhattacharya ◽  
Leonardo Marazzi
Keyword(s):  
Differential Equation ◽  
Viscosity Solutions ◽  
Parabolic Differential Equation ◽  
Degenerate Parabolic

scholarly journals On the Cauchy problem for a degenerate parabolic differential equation

1998 ◽  
Vol 21 (3) ◽  
pp. 555-558
Author(s):  
Ahmed El-Fiky
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Parabolic Equation ◽  
Degenerate Parabolic Equation ◽  
Parabolic Differential Equation ◽  
The Cauchy Problem ◽  
Uniqueness Of The Solution ◽  
Degenerate Parabolic

The aim of this work is to prove the existence and the uniqueness of the solution of a degenerate parabolic equation. This is done using H. Tanabe and P.E. Sobolevsldi theory.

scholarly journals Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations

2005 ◽  
Vol 2005 (6) ◽  
pp. 607-617 ◽  
Author(s):  
Ismail Kombe
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Parabolic Partial Differential Equation ◽  
Nonlinear Parabolic ◽  
Nonlinear Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Nonlinear Degenerate

We will investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:∂u/∂t=ℒu+V(w)up−1inΩ×(0,T),1<p<2,u(w,0)=u0(w)≥0inΩ,u(w,t)=0on∂Ω×(0,T)whereℒis the subellipticp-Laplacian andV∈Lloc1(Ω).

Formalization and computational aspects of image analysis

Acta Numerica ◽  
1994 ◽  
Vol 3 ◽  
pp. 1-59 ◽  
Author(s):  
Luis Alvarez ◽  
Jean Michel Morel
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Image Analysis ◽  
Image Segmentation ◽  
Multiscale Analysis ◽  
Parabolic Differential Equation ◽  
The Past ◽  
Computational Aspects ◽  
Shape Analyses ◽  
New Algorithms

In this article we shall present a unified and axiomatized view of several theories and algorithms of image multiscale analysis (and low level vision) which have been developed in the past twenty years. We shall show that under reasonable invariance and assumptions, all image (and shape) analyses can be reduced to a single partial differential equation. In the same way, movie analysis leads to a single parabolic differential equation. We discuss some applications to image segmentation and movie restoration. The experiments show how accurate and invariant the numerical schemes must be and we compare several (old and new) algorithms by discussing how well they match the axiomatic invariance requirements.

scholarly journals STATIONARY STOCHASTIC VISCOSITY SOLUTIONS OF SPDEs

2011 ◽  
Vol 11 (04) ◽  
pp. 691-713 ◽  
Author(s):  
QI ZHANG
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Viscosity Solution ◽  
Viscosity Solutions ◽  
Infinite Horizon ◽  
Parabolic Type ◽  
Regularity Of Solutions ◽  
Doubly Stochastic

In this paper, we construct the pathwise stationary stochastic viscosity solution of a parabolic type SPDE by backward doubly stochastic differential equation (BDSDE) on infinite horizon. For this, we study the existence, uniqueness and regularity of solutions of infinite horizon BDSDEs and their pathwise stationary property. Then by the correspondence between stochastic viscosity solutions of SPDEs and real-valued solutions of BDSDEs on infinite horizon, the stationary property is transferred from BDSDEs to SPDEs.

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