Integral equation for the causal distributions and their self-similar asymptotic behavior in the ladder ?3 model

1980 ◽  
Vol 45 (3) ◽  
pp. 1041-1048
Author(s):  
A. N. Kvinikhidze ◽  
B. A. Magradze ◽  
V. A. Matveev ◽  
M. A. Mestvirishvili ◽  
A. N. Tavkhelidze
Keyword(s):  
Integral Equation ◽  
Asymptotic Behavior ◽  
Self Similar

scholarly journals Asymptotic Behavior of Solutions of Integral Equations with Homogeneous Kernels

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 180
Author(s):  
Oleg Avsyankin
Keyword(s):  
Integral Equation ◽  
Asymptotic Behavior ◽  
Integral Equations ◽  
Spherical Harmonics ◽  
Special Class ◽  
Continuous Functions ◽  
Asymptotic Behavior Of Solutions ◽  
Free Term ◽  
Research Technique ◽  
Multidimensional Integral

The multidimensional integral equation of second kind with a homogeneous of degree (−n) kernel is considered. The special class of continuous functions with a given asymptotic behavior in the neighborhood of zero is defined. It is proved that, if the free term of the integral equation belongs to this class and the equation itself is solvable, then its solution also belongs to this class. To solve this problem, a special research technique is used. The above-mentioned technique is based on the decomposition of both the solution and the free term in spherical harmonics.

scholarly journals Self-Similar Blow-Up Solutions of the KPZ Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Alexander Gladkov
Keyword(s):  
Asymptotic Behavior ◽  
Blow Up ◽  
Kpz Equation ◽  
Self Similar ◽  
The Kpz Equation ◽  
Similar Solutions

Self-similar blow-up solutions for the generalized deterministic KPZ equationut=uxx+|ux|qwithq>2are considered. The asymptotic behavior of self-similar solutions is studied.

Universal self-similar asymptotic behavior of optical bump spreading in random medium atop incoherent background: reply

2020 ◽  
Vol 45 (13) ◽  
pp. 3511
Author(s):  
Xiaofei Li ◽  
Sergey A. Ponomarenko ◽  
Zhiheng Xu ◽  
Fei Wang ◽  
Yangjian Cai ◽  
...  
Keyword(s):  
Asymptotic Behavior ◽  
Random Medium ◽  
Self Similar

SELF-SIMILARITY OF SOLUTIONS TO INTEGRAL AND DIFFERENTIAL EQUATIONS WITH RESPECT TO A FRACTAL MEASURE

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950014
Author(s):  
H. KUNZE ◽  
D. LA TORRE ◽  
F. MENDIVIL ◽  
E. R. VRSCAY
Keyword(s):  
Integral Equation ◽  
Iterated Function System ◽  
Differential Forms ◽  
Self Similarity ◽  
Similar Measure ◽  
Picard Operator ◽  
Convergence Results ◽  
Iterated Function ◽  
Classical Integral ◽  
Self Similar

In this paper, we study solutions of a variation of a classical integral equation (based on the Picard operator) in which Lebesgue measure is replaced by a self-similar measure [Formula: see text]. Our main interest is in the fractal nature of the solutions and we use Iterated Function System (IFS) tools to investigate the behavior and self-similarity of these solutions. Both the integral and differential forms of the equation are discussed since each brings useful insights. Several convergence results are provided along with illustrative examples that show the applications of the theory when the underlying fractal object is the celebrated Cantor set. Additionally we show that the solution to our integral equation inherits self-similarity from the defining measure [Formula: see text].

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