scholarly journals A remark on my paper “A Unique continuation theorem of a parabolic differential equation”

1960 ◽  
Vol 36 (3) ◽  
pp. 133-135 ◽  
Author(s):  
Taira Shirota
Keyword(s):  
Differential Equation ◽  
Unique Continuation ◽  
Continuation Theorem ◽  
Parabolic Differential Equation

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 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.

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