Existence and uniqueness of distributional solution for semilinear fractional elliptic equation involving new operator and some numerical results

2021 ◽  
Author(s):  
Chaima Saadi ◽  
Hakim Lakhal ◽  
Kamel Slimani ◽  
Sara Dob
Keyword(s):  
Elliptic Equation ◽  
Existence And Uniqueness ◽  
Numerical Results ◽  
Distributional Solution

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

scholarly journals On the Existence and Uniqueness ofRv-Generalized Solution for Dirichlet Problem with Singularity on All Boundary

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
V. Rukavishnikov ◽  
E. Rukavishnikova
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Input Data ◽  
Generalized Solution ◽  
Two Dimensional ◽  
Order Elliptic Equation ◽  
Second Order Elliptic Equation ◽  
Dimensional Domain

The existence and uniqueness of theRv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.

scholarly journals ONE-VALUED SOLVABILITY OF A NONLOCAL PROBLEM FOR THE AXISYMMETRIC HELMHOLTZ EQUATION

2017 ◽  
Vol 17 (2) ◽  
pp. 5-14
Author(s):  
A.A. Abashkin
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Problem ◽  
Degenerate Elliptic Equation ◽  
Nonlocal Boundary Value Problem ◽  
Degenerate Elliptic ◽  
Uniqueness Of A Solution

A nonlocal boundary value problem for degenerate elliptic equation is considered. Boundary value of this problem considerably depend on low derivativecoefficient changes. Existence and uniqueness of a solution are proved.

Existence and uniqueness of solutions of an A-harmonic elliptic equation

2019 ◽  
Vol 56 (1) ◽  
pp. 13-21
Author(s):  
Mouna Kratou
Keyword(s):  
Weak Solution ◽  
Elliptic Equation ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions

Abstract This paper deals with the existence and uniqueness of weak solution of a problem which involves a class of A-harmonic elliptic equations of nonhomogeneous type. Under appropriate assumptions on the function f, our main results are obtained by using Browder Theorem.

scholarly journals AN INVERSE BOUNDARY VALUE PROBLEM FOR A SECOND ORDER ELLIPTIC EQUATION IN A RECTANGLE

2014 ◽  
Vol 19 (2) ◽  
pp. 241-256 ◽  
Author(s):  
Yashar T. Mehraliyev ◽  
Fatma Kanca
Keyword(s):  
Inverse Problem ◽  
Elliptic Equation ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Order Elliptic Equation ◽  
Inverse Boundary ◽  
Numerical Tests ◽  
Second Order Elliptic Equation

In this paper, the inverse problem of finding a coefficient in a second order elliptic equation is investigated. The conditions for the existence and uniqueness of the classical solution of the problem under consideration are established. Numerical tests using the finite-difference scheme combined with an iteration method is presented and the sensitivity of this scheme with respect to noisy overdetermination data is illustrated.

scholarly journals On the Dirichlet Problem with Corner Singularity

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1870
Author(s):  
Viktor A. Rukavishnikov ◽  
Elena I. Rukavishnikova
Keyword(s):  
Approximate Solution ◽  
Dirichlet Problem ◽  
Numerical Methods ◽  
Elliptic Equation ◽  
Existence And Uniqueness ◽  
Generalized Solution ◽  
Corner Singularity

We consider the Dirichlet problem for an elliptic equation with a singularity. The singularity of the solution to the problem is caused by the presence of a re-entrant corner at the boundary of the domain. We define an Rν-generalized solution for this problem. This allows for the construction of numerical methods for finding an approximate solution without loss of accuracy. In this paper, the existence and uniqueness of the Rν-generalized solution in set W∘2,α1(Ω,δ) is proven. The Rν-generalized solution is the same for different parameters ν.

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