scholarly journals The Solvability of First Type Boundary Value Problem for a Schrödinger Equation

2020 ◽  
Vol 5 (1) ◽  
pp. 211-220
Author(s):  
Nigar Yildirim Aksoy
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
A Priori ◽  
A Priori Estimate ◽  
Uniqueness Theorems ◽  
Priori Estimate ◽  
Type Boundary

AbstractThe paper presents an first type boundary value problem for a Schrödinger equation. The aim of paper is to give the existence and uniqueness theorems of the boundary value problem using Galerkin’s method. Also, a priori estimate for its solution is given.

A priori estimate for the solution of a nonlocal boundary value problem for the McKendrick - von Foerster equation of fractional order

2020 ◽  
Vol 20 (1) ◽  
pp. 9-14
Author(s):  
R.Z. Berezgova ◽  
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
A Priori Estimate ◽  
Time Variable ◽  
Nonlocal Boundary Value Problem ◽  
Priori Estimate

In this paper, by the method of energy inequalities, an a priori estimate for the solution of the nonlocal boundary value problem is obtained for the generalized Mackendrick - von Foerster equation with the Caputo operator with respect to the time variable.

scholarly journals On three-point boundary value problem with a weighted integral condition for a class of singular parabolic equations

2002 ◽  
Vol 7 (10) ◽  
pp. 517-530 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Point Boundary ◽  
Priori Estimate ◽  
Weighted Integral ◽  
Singular Parabolic Equations

We deal with a three point boundary value problem for a class of singular parabolic equations with a weighted integral condition in place of one of standard boundary conditions. We will first establish an a priori estimate in weighted spaces. Then, we prove the existence, uniqueness, and continuous dependence of a strong solution.

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

scholarly journals On a class of singular hyperbolic equation with a weighted integral condition

1999 ◽  
Vol 22 (3) ◽  
pp. 511-519 ◽  
Author(s):  
Said Mesloub ◽  
Abdelfatah Bouziani
Keyword(s):  
Hyperbolic Equation ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Nonlocal Condition ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Priori Estimate ◽  
Weighted Integral

In this paper, we study a mixed problem with a nonlocal condition for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.

scholarly journals Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics

2013 ◽  
Vol 469 (2159) ◽  
pp. 20130341 ◽  
Author(s):  
Elena I. Kaikina
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Boundary Data ◽  
Schrodinger Equation ◽  
Large Time ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value ◽  
Robin Boundary

We consider the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with inhomogeneous Robin boundary data. We study traditionally important problems of the theory of nonlinear partial differential equations, such as the global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behaviour of solutions for large time.

scholarly journals On an initial-boundary value problem for the nonlinear Schrödinger equation

1979 ◽  
Vol 2 (3) ◽  
pp. 503-522 ◽  
Author(s):  
Herbert Gajewski
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Initial Boundary Value

We study an initial-boundary value problem for the nonlinear Schrödinger equation, a simple mathematical model for the interaction between electromagnetic waves and a plasma layer. We prove a global existence and uniqueness theorem and establish a Galerkin method for solving numerically the problem.

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