Open AccessPROPERTIES OF A CERTAIN LOADED INTEGRAL OPERATOR WITH WEIGHT
Author(s) -
Владимир Игоревич Усков,
Arina Panteleeva
Publication year - 2021
Publication title -
voronežskij naučno-tehničeskij vestnik
Language(s) - English
Resource type - Journals
ISSN - 2311-8873
DOI - 10.34220/2311-8873-2021-4-4-4-10
Subject(s) - mathematics , operator (biology) , volterra integral equation , mathematical analysis , integral equation , elasticity (physics) , semigroup , semi elliptic operator , differential operator , physics , biochemistry , chemistry , repressor , transcription factor , gene , thermodynamics
In this paper, we consider a certain integral operator with a weight, loaded with operator term. It acts in the space of continuous functions. The conditions under which this operator is limited are determined, the form of its semigroup is es-tablished. The Cauchy problem for an integro-differential equation is considered as an application. Such equations arise in the theory of elasticity and models of biological processes: Proctor's problem on the equilibrium of an elastic beam, Volterra's problem on torsional vibrations, Prandtl's problem for calculating an airplane wing, in analysis of economic models, etc.