Geodesic
A method for representing solutions of the Cauchy problem for linear partial differential equations
Sbornik. Mathematics, Tome 209 (2018) no. 2, pp. 222-240 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A method for solving the Cauchy problem for certain types of linear partial differential equations and pseudo-differential equations is proposed. A class of functions is specified for which the existence and uniqueness of solutions is proved. Applications of the results in applied problems are considered. Bibliography: 8 titles.
Keywords: Hopf equation, resolving operator, generalized functions with compact support.
Mots-clés : Fourier transform 
@article{SM_2018_209_2_a4,
     author = {V. I. Gishlarkaev},
     title = {A~method for representing solutions of the {Cauchy} problem for linear partial differential equations},
     journal = {Sbornik. Mathematics},
     pages = {222--240},
     year = {2018},
     volume = {209},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_2_a4/}
}
TY  - JOUR
AU  - V. I. Gishlarkaev
TI  - A method for representing solutions of the Cauchy problem for linear partial differential equations
JO  - Sbornik. Mathematics
PY  - 2018
SP  - 222
EP  - 240
VL  - 209
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_2018_209_2_a4/
LA  - en
ID  - SM_2018_209_2_a4
ER  - 
%0 Journal Article
%A V. I. Gishlarkaev
%T A method for representing solutions of the Cauchy problem for linear partial differential equations
%J Sbornik. Mathematics
%D 2018
%P 222-240
%V 209
%N 2
%U http://geodesic.mathdoc.fr/item/SM_2018_209_2_a4/
%G en
%F SM_2018_209_2_a4
V. I. Gishlarkaev. A method for representing solutions of the Cauchy problem for linear partial differential equations. Sbornik. Mathematics, Tome 209 (2018) no. 2, pp. 222-240. http://geodesic.mathdoc.fr/item/SM_2018_209_2_a4/

[1] W. Feller, An introduction to probability theory and its applications, v. II, John Wiley Sons, Inc., New York–London–Sydney, 1966, xviii+626 pp. | MR | MR | Zbl | Zbl

[2] A. D. Polyanin, Spravochnik po lineinym uravneniyam matematicheskoi fiziki, Fizmatlit, M., 2001, 576 pp. | Zbl

[3] M. I. Vishik, A. V. Fursikov, Mathematical problems of statistical hydromechanics, Math. Appl. (Soviet Ser.), 9, Kluwer Acad. Publ., Dordrecht, 1988, vii+576 pp. | DOI | MR | MR | Zbl | Zbl

[4] E. Hopf, “Statistical hydromechanics and functional calculus”, J. Rational Mech. Anal., 1 (1952), 87–123 | MR | Zbl

[5] M. Reed, B. Simon, Methods of modern mathematical physics, v. II, Fourier analysis, self-adjointness, Academic Press, New York–London, 1975, xv+361 pp. | MR | MR | Zbl

[6] Ph. Hartman, Ordinary differential equations, John Wiley Sons, Inc., New York–London–Sydney, 1964, xiv+612 pp. | MR | MR | Zbl | Zbl

[7] L. Hörmander, The analysis of linear partial differential operators, v. I, Grundlehren Math. Wiss., 256, Distribution theory and Fourier analysis, Springer-Verlag, Berlin, 1983, ix+391 pp. | DOI | MR | MR | Zbl | Zbl

[8] G. E. Shilov, Matematicheskii analiz, Vtoroi spetsialnyi kurs, 2-e izd., Izd-vo Mosk. un-ta, M., 1984, 208 pp. | MR | Zbl