Singulyarnye integral'nye uravneniya so slozhnoy osobennost'yu v yadre: teoriya, algoritmy i prilozheniya (Russian Edition)

 
9783847308980: Singulyarnye integral'nye uravneniya so slozhnoy osobennost'yu v yadre: teoriya, algoritmy i prilozheniya (Russian Edition)

Singulyarnye integral'nye uravneniya vstrechayutsya vo mnogikh razdelakh matematicheskoy fiziki, eto sposobstvuet i razvitiyu teorii, i poisku effektivnykh algoritmov ikh chislennogo resheniya. V knige rassmatrivayutsya singulyarnye integral'nye uravneniya, yadra kotorykh imeyut osobennosti logarifmicheskogo ili stepennogo tipa, a takzhe odnovremenno slabye i sil'nye osobennosti v razlichnykh sochetaniyakh. Sushchestvenno ispol'zuetsya svyaz' mezhdu resheniyami takikh singulyarnykh uravneniy i resheniyami integral'nykh uravneniy s yadrom Koshi. Eta svyaz' zadaetsya, kak pravilo, takzhe v forme integral'nogo uravneniya. Novye klassy uravneniy so slozhnoy osobennost'yu v yadre polucheny v sluchae, kogda porozhdayushchee uravnenie yavlyaetsya integral'nym uravneniem Vol'terra s vyrozhdennym yadrom. Obsuzhdayutsya nekotorye prostye algoritmy chislennogo resheniya singulyarnykh integral'nykh uravneniy, osnovannye na global'nom vydelenii osobennostey iz singulyarnogo integrala. Rassmotren ryad zadach ploskoy kontaktnoy teorii uprugosti i nekotorye granichnye zadachi dlya uprugikh tel s defektami. Dlya studentov, aspirantov i nauchnykh rabotnikov, interesuyushchikhsya teoriey singulyarnykh integral'nykh uravneniy, algoritmami ikh chislennogo resheniya i prilozheniyami.

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About the Author:

Pleshchinskiy Nikolay Borisovich, doktor fiziko-matematicheskikh nauk, professor, zaveduyushchiy kafedroy prikladnoy matematiki Kazanskogo (Privolzhskogo) federal'nogo universiteta. Oblast' nauchnykh interesov - matematicheskoe modelirovanie i matematicheskaya fizika, uravneniya s chastnymi proizvodnymi i integral'nye uravneniya.

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