Linear Hyperbolic Functional-Differential Equations with Essentially Bounded Right-Hand Side

Alexander Domoshnitsky, Alexander Lomtatidze, Abraham Maghakyan and Jiří Šremr

Abstract and Applied Analysis, 2011, vol. 2011, 1-26

Abstract:

Theorems on the unique solvability and nonnegativity of solutions to the characteristic initial value problem ð ‘¢ ( 1 , 1 ) ( ð ‘¡ , ð ‘¥ ) = â„“ 0 ( ð ‘¢ ) ( ð ‘¡ , ð ‘¥ ) + â„“ 1 ( ð ‘¢ ( 1 , 0 ) ) ( ð ‘¡ , ð ‘¥ ) + â„“ 2 ( ð ‘¢ ( 0 , 1 ) ) ( ð ‘¡ , ð ‘¥ ) + ð ‘ž ( ð ‘¡ , ð ‘¥ ) , ð ‘¢ ( ð ‘¡ , ð ‘ ) = ð ›¼ ( ð ‘¡ ) for ð ‘¡ ∈ [ ð ‘Ž , ð ‘ ] , ð ‘¢ ( ð ‘Ž , ð ‘¥ ) = ð ›½ ( ð ‘¥ ) f o r ð ‘¥ ∈ [ ð ‘ , ð ‘‘ ] given on the rectangle [ ð ‘Ž , ð ‘ ] × [ ð ‘ , ð ‘‘ ] are established, where the linear operators â„“ 0 , â„“ 1 , â„“ 2 map suitable function spaces into the space of essentially bounded functions. General results are applied to the hyperbolic equations with essentially bounded coefficients and argument deviations.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:242965

DOI: 10.1155/2011/242965

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