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, issue 1

Abstract: Theorems on the unique solvability and nonnegativity of solutions to the characteristic initial value problem u(1,1)(t, x) = ℓ0(u)(t, x) + ℓ1(u(1,0))(t, x) + ℓ2(u(0,1))(t, x) + q(t, x), u(t, c) = α(t) for t ∈ [a, b], u(a, x) = β(x) for x ∈ [c, d] given on the rectangle [a, b]×[c, d] are established, where the linear operators ℓ0, ℓ1, ℓ2 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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https://doi.org/10.1155/2011/242965

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:242965

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