scholarly journals On the Boundedness of Solution of the Parabolic Differential Equation with Time Involution

2020 ◽  
Vol 22 (2) ◽  
pp. 339-344
Author(s):  
Allaberen Ashyralyev ◽  
◽  
Amer Ahmed ◽  
Keyword(s):  
Differential Equation ◽  
Parabolic Differential Equation ◽  
Boundedness Of Solution

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.

scholarly journals Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Asker Hanalyev
Keyword(s):  
Differential Equation ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Continuous Functions ◽  
Parabolic Differential Equation ◽  
Well Posedness ◽  
Nonlocal Boundary Value Problem ◽  
Hölder Condition ◽  
Linear Positive Operator

The nonlocal boundary value problem for the parabolic differential equationv'(t)+A(t)v(t)=f(t)  (0≤t≤T),  v(0)=v(λ)+φ,  0<λ≤Tin an arbitrary Banach spaceEwith the dependent linear positive operatorA(t)is investigated. The well-posedness of this problem is established in Banach spacesC0β,γ(Eα-β)of allEα-β-valued continuous functionsφ(t)on[0,T]satisfying a Hölder condition with a weight(t+τ)γ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

scholarly journals Exact variational representations for the solution of the simple parabolic equation

1971 ◽  
Vol 5 (3) ◽  
pp. 305-314
Author(s):  
R.S. Anderssen
Keyword(s):  
Differential Equation ◽  
Fourier Series ◽  
Parabolic Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Parabolic Differential Equation ◽  
Initial Boundary Value Problems ◽  
Series Representations ◽  
Initial Boundary Value

By constructing a special set of A-orthonormal functions, it is shown that, under certain smoothness assumptions, the variational and Fourier series representations for the solution of first initial boundary value problems for the simple parabolic differential equation coincide. This result is then extended in order to construct a variational representation for the solution of a very general first initial boundary value problem for this equation.

scholarly journals A parabolic differential equation with unbounded piecewise constant delay

1992 ◽  
Vol 15 (2) ◽  
pp. 339-346 ◽  
Author(s):  
Joseph Wiener ◽  
Lokenath Debnath
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Difference Equations ◽  
Infinite Delay ◽  
Parabolic Differential Equation ◽  
Constant Delay ◽  
Partial Differential ◽  
Piecewise Constant ◽  
Greatest Integer Function

A partial differential equation with the argument[λt]is studied, where[•]denotes the greatest integer function. The infinite delayt−[λt]leads to difference equations of unbounded order.

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