Hyperbolic problems in three independent variables: Mathematical analysis and constructive methods

We consider initial-boundary value problems associated with nonlinear hyperbolic partial differential equations in three independent variables in a unified setting, wherein the forcing function is a sum of two monotonic functions. After deriving the required mathematical theory of hyperbolic partial...

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Bibliographic Details
Published in:Nonlinear analysis 2009-12, Vol.71 (12), p.e1796-e1801
Main Authors: Dezern, D.H., Pandit, S.G., Vyas, U.D.
Format: Article
Language:English
Subjects:
Boundary value problems
Construction
Coupled lower–upper solutions
Coupled minimal–maximal solutions
Hyperbolic partial differential inequality
Independent variables
Inequalities
Initial value problems
Iterative methods
Mathematical analysis
Monotone iterative technique
Nonlinearity
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Summary:We consider initial-boundary value problems associated with nonlinear hyperbolic partial differential equations in three independent variables in a unified setting, wherein the forcing function is a sum of two monotonic functions. After deriving the required mathematical theory of hyperbolic partial differential inequalities, we employ natural lower–upper solutions and two types of coupled lower–upper solutions, to derive linear iterative schemes which converge uniformly and monotonically to the minimal–maximal solutions or the coupled minimal–maximal solutions of the nonlinear problem. Examples are given to illustrate the results.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.02.058