Operatory monotonnogo tipa: Nelineynye uravneniya, variatsionnye neravenstva, obobshchennaya kraevaya zadacha, metod fiktivnykh oblastey, approksimatsii (Russian Edition)

Description

V nastoyashchey rabote rassmatrivayutsya nekotorye obobshcheniya monotonnykh operatorov - (M) operatory ili operatory monotonnogo tipa. Izuchayutsya nelineynye operatornye uravneniya i variatsionnye neravenstva s operatorami tipa (M). Dokazyvayutsya nekotorye nekoertsitivnye usloviya razreshimosti dlya takikh uravneniy i variatsionnykh neravenstv. Stroyatsya approksimatsionnye skhemy dlya priblizhennogo resheniya obobshchennykh kraevykh zadach i dokazyvayutsya otsenki skorosti skhodimosti dlya nikh. Pokazyvaetsya, chto metod fiktivnykh oblastey resheniya kraevykh zadach matematicheskoy fiziki s ellipticheskimi differentsial'nymi operatorami yavlyaetsya nekotoroy approksimatsiey obobshchennoy kraevoy zadachi v banakhovom prostranstve.