Asymptotic behavior of the normalized eigenfunctions of a Sturm-Liouville type operator for partial differential equations in theN-dimensional ball

1999 ◽  
Vol 65 (4) ◽  
pp. 519-521
Author(s):  
G. A. Aigunov
Keyword(s):  
Asymptotic Behavior ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Type Operator ◽  
Liouville Type ◽  
Partial Differential ◽  
Sturm Liouville ◽  
Dimensional Ball

scholarly journals Existence of Positive Solutions and Its Asymptotic Behavior of (p(x), q(x))-Laplacian Parabolic System

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 332 ◽  
Author(s):  
Hamza Medekhel ◽  
Salah Boulaaras ◽  
Khaled Zennir ◽  
Ali Allahem
Keyword(s):  
Asymptotic Behavior ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Parabolic System ◽  
Stationary Case ◽  
Partial Differential ◽  
Existence Of Positive Solutions

This paper deals with the existence of positively solution and its asymptotic behavior for parabolic system of ( p ( x ) , q ( x ) ) -Laplacian system of partial differential equations using a sub and super solution according to some given boundary conditions, Our result is an extension of Boulaaras’s works which studied the stationary case, this idea is new for evolutionary case of this kind of problem.

scholarly journals The probabilistic point of view on the generalized fractional partial differential equations

2019 ◽  
Vol 22 (3) ◽  
pp. 543-600 ◽  
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Monte Carlo Simulation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Point Of View ◽  
Fractional Partial Differential Equations ◽  
Exit Times ◽  
Liouville Type ◽  
Partial Differential ◽  
Path Integral Representation ◽  
Probabilistic Point

Abstract This paper aims at unifying and clarifying the recent advances in the analysis of the fractional and generalized fractional Partial Differential Equations of Caputo and Riemann-Liouville type arising essentially from the probabilistic point of view. This point of view leads to the path integral representation for the solutions of these equations, which is seen to be stable with respect to the initial data and key parameters and is directly amenable to numeric calculations (Monte-Carlo simulation). In many cases these solutions can be compactly presented via the wide class of operator-valued analytic functions of the Mittag-Leffler type, which are proved to be expressed as the Laplace transforms of the exit times of monotone Markov processes.

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