First-Order Partial Differential Equation with a Nonlocal Boundary Condition

In this paper, the initial value problem for the first-order partial differential equation with the nonlocal boundary condition is studied. The positivity of the space operator A x generated by this problem in interpolation spaces is established. The structure interpolation spaces of this space oper...

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Bibliographic Details
Published in:Numerical functional analysis and optimization 2017-10, Vol.38 (10), p.1373-1389
Main Authors: Erdogan, Abdullah S., Tekalan, Sueda N.
Format: Article
Language:English
Subjects:
Boundary conditions
Differential equations
Hyperbolic system of equations
Interpolation
interpolation spaces
nonlocal boundary value problems
Partial differential equations
positivity
stability estimates
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Summary:In this paper, the initial value problem for the first-order partial differential equation with the nonlocal boundary condition is studied. The positivity of the space operator A x generated by this problem in interpolation spaces is established. The structure interpolation spaces of this space operator is investigated. The positivity of this space operator in Hölder spaces is established. In applications, the stability estimates for the first-order partial differential equation with the nonlocal boundary condition are obtained.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2017.1317002