Strict definition of improper integrals by hadamard that are found in mathematical models of aerodynamics for the whole degrees of a singularity

Mathematics


Аuthors

Smirnov V. U.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

Abstract

Improper integrals by Hadamard that are found in mathematical models of aerodynamics and other problems of mathematical physics are studied. The case of a strong singularity inside of a segment of integration is considered. The whole degrees of a singularity are researched. The existence theorem of an improper integral by Hadamard in the considered case is proved. Strict definition of an integral in terms of final value by Hadamard for the whole degrees of a singularity is given. Explicit expression for an integral by Hadamard is obtained. The expression for an integral by Hadamard that doesn't contain improper integrals convenient for application in mathematical models is obtained also.


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