Geodesic
On the Cauchy problem for linear PDEs with retarded arguments at derivatives
Krzysztof A. Topolski1
1 Institute of Mathematics University of Gdańsk 80-952 Gdańsk, Poland
Annales Polonici Mathematici, Tome 113 (2015) no. 3, pp. 269-282.

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

We present an existence theorem for the Cauchy problem related to linear partial differential-functional equations of an arbitrary order. The equations considered include the cases of retarded and deviated arguments at the derivatives of the unknown function. In the proof we use Tonelli's constructive method. We also give uniqueness criteria valid in a wide class of admissible functions. We present a set of examples to illustrate the theory.
DOI : 10.4064/ap113-3-4
Keywords: present existence theorem cauchy problem related linear partial differential functional equations arbitrary order equations considered include cases retarded deviated arguments derivatives unknown function proof tonellis constructive method uniqueness criteria valid wide class admissible functions present set examples illustrate theory

Krzysztof A. Topolski 1

1 Institute of Mathematics University of Gdańsk 80-952 Gdańsk, Poland 
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Krzysztof A. Topolski. On the Cauchy problem for linear PDEs
 with retarded arguments at derivatives. Annales Polonici Mathematici, Tome 113 (2015) no. 3, pp. 269-282. doi : 10.4064/ap113-3-4. http://geodesic.mathdoc.fr/articles/10.4064/ap113-3-4/

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