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A non-linear Goursat problem for a 4th order polyvibrating equation

Published online by Cambridge University Press:  14 November 2011

Andrzej Borzymowski
Andrzej Borzymowski
Affiliation:
Warsaw University of Technology, PI. Jedności Robotniczej 1, Warsaw, Poland
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Synopsis

In the paper the existence is proved of a solution of a non-linear Goursat problem for a 4th order partial differential equation with the boundary conditions given on four curves emanating from a common point. The problem is reduced to a system of integro-functional equations and then Schauder's fixed point theorem is applied.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 1-2 , 1982 , pp. 153 - 164
Copyright
Copyright © Royal Society of Edinburgh 1982

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References

1Bielecki, A. and Kisyńiski, J.. Sur le problème de E. Goursat relatif à 1'équation ∂2z/∂x ∂y = f(x,y).. Ann. Univ. Mariae Curie-Skłodowska Sect. A 10 (1956), 99–126.Google Scholar
2Borzymowski, A.. A Goursat problem for a polyvibrating equation of D. Mangeron. Funkcial. Ekvac. 23 (1980), 1–16.Google Scholar
3Cinquini-Cibrario, M. and Cinquini, S.. Equazioni a derivate parziali di tipo iperbolico (Rome: Edizioni Cremonese, 1964).Google Scholar
4Haack, W. and Hellwig, G.. Über Systeme hyperbolischer Differential-gleichungen erster Ordnung I, II. Math Z. 53 (1950), 244–266; 340–356.CrossRefGoogle Scholar
5Hecquet, G.. Etude de quelques problemes d'existence globale concernant l'équation ∂r−s/∂xr ∂ys = f(x,y,u ∂u/∂x, ∂u/∂y,…,∂p+qu/∂xp ∂y,q …), 0 ≦ p ≦ r; 0 ≦ q ≦ s; p + q ≦ r + s.. Ann. Mat. Pura Appl. 113 (1977), 173–197.CrossRefGoogle Scholar
6Hellwig, G.. Über Systeme hyperbolischer Differential-gleichungen erster Ordnung. Math. Z. 68 (1958), 325–337.CrossRefGoogle Scholar
7Kuczma, M.. Functional equations in a single variable (Warsaw: PWN, 1968).Google Scholar
8Oğuztöreli, M. N. and Easwaran, S.. A Goursat problem for a high order Mangeron equation. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 50 (1971), 650–653.Google Scholar
9Oğuztöreli, M. N.. Sur le problème de Goursat pour une equation de Mangeron d'ordre superieur I, II. Bull. Acad. Roy. Belg. Cl. Sci. 58 (1972), 464–471; 577–582.Google Scholar
10. Radochova, V.. Die Lösung der partiellen differential-gleichung uxxtt = A(t, x)uxx +B(t, u)utt mit gewissen nebenbedingungen. Časopis Pěst. Mat. 98 (1973), 388–397.Google Scholar
11Walter, W.. Differential and integral inequalities (Berlin: Springer-Verlag, 1970).CrossRefGoogle Scholar
12Sjöstrand, O.. Sur le problème de M. Goursat pour les équations aux dérivées partielles du seconde ordre ou de Vordre supérieure (Göteborg: 1929).Google Scholar