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On the characteristic initial-value problem for linear partial functional-differential equations of hyperbolic type

Part of: Hyperbolic equations and systems

Published online by Cambridge University Press:  02 February 2009

Jiří Šremr
Jiří Šremr
Affiliation:
Mathematical Institute, Academy of Sciences of the Czech Republic, Žižkova 22, 61662 Brno, Czech Republic (sremr@ipm.cz)
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Abstract

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Theorems on the Fredholm alternative and well-posedness of the characteristic initial-value problem

are established, where l : C(;ℝ) is a linear bounded operator, q ∈ L(;ℝ), ϕ:[a,b]→ℝ, ψ:[c,d]→ℝ are absolutely continuous functions and =[a,b]×[c,d]. Some solvability conditions of the problem considered are also given.

Keywords

functional-differential equation of hyperbolic typecharacteristic initial-value problemFredholm alternativewell-posednessexistence of solutions

MSC classification

Secondary: 35L15: Initial value problems for second-order hyperbolic equations 35L10: Second-order hyperbolic equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 1 , February 2009 , pp. 241 - 262
Copyright
Copyright © Edinburgh Mathematical Society 2009