Geodesic
On the local Cauchy problem for first order partial differential functional equations
El/zbieta Pu/xniakowska-Ga/luch1
1 Institute of Mathematics University of Gda/nsk Wit Stwosz Street 57 80-952 Gda/nsk, Poland
Annales Polonici Mathematici, Tome 98 (2010) no. 1, pp. 39-61

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A theorem on the existence of weak solutions of the Cauchy problem for first order functional differential equations defined on the Haar pyramid is proved. The initial problem is transformed into a system of functional integral equations for the unknown function and for its partial derivatives with respect to spatial variables. The method of bicharacteristics and integral inequalities are applied. Differential equations with deviated variables and differential integral equations can be obtained from the general theory by specializing given operators.
DOI : 10.4064/ap98-1-3
Keywords: theorem existence weak solutions cauchy problem first order functional differential equations defined haar pyramid proved initial problem transformed system functional integral equations unknown function its partial derivatives respect spatial variables method bicharacteristics integral inequalities applied differential equations deviated variables differential integral equations obtained general theory specializing given operators

El/zbieta Pu/xniakowska-Ga/luch 1

1 Institute of Mathematics University of Gda/nsk Wit Stwosz Street 57 80-952 Gda/nsk, Poland 
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El/zbieta Pu/xniakowska-Ga/luch. On the local Cauchy problem for first order
 partial differential functional equations. Annales Polonici Mathematici, Tome 98 (2010) no. 1, pp. 39-61. doi: 10.4064/ap98-1-3

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