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On the structure of the set of solutions of the Darboux problem for hyperbolic equations

Published online by Cambridge University Press:  20 January 2009

F. S. de Blasi  and
J. Myjak
F. S. de Blasi
Affiliation:
Dipartimento di Matematica, Università di Roma II, Via O. Raimondo, 00173 Roma, Italy
J. Myjak
Affiliation:
Instytut Matematyki AGHAl. Mickiewicza 3030-059 KrakówPoland
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Consider the Darboux problem

where φ,ψ:I→Rd (I=[0,1]) are given absolutely continuous functions with φ(0)=ψ(0), and the mapping f : Q × Rd→Rd (Q = I × I) satisfies the following hypotheses:

(A1) f(.,.,z) is measurable for every z ∈ Rd;

(A2) f(x, y,.) is continuous for a.a. (almost all) (x, y) ∈ Q;

(A3) there exists an integrable function α:Q →[0, + ∞) such that |f(x, y, z)|≦α(x, y) for every (x, y, z)∈ Q × Rd.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 1 , February 1986 , pp. 7 - 14
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

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