Open AccessQuasilinear integrodifferential Bernoulli-type equations
Author(s) -
V. L. Vaskevich,
И. В. Шваб
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1391/1/012075
Subject(s) - mathematics , iterated function , bernoulli's principle , initial value problem , cauchy problem , interval (graph theory) , function (biology) , domain (mathematical analysis) , mathematical analysis , cauchy distribution , type (biology) , real line , convergence (economics) , space (punctuation) , quadratic equation , variable (mathematics) , class (philosophy) , combinatorics , ecology , linguistics , philosophy , geometry , evolutionary biology , artificial intelligence , economic growth , computer science , engineering , economics , biology , aerospace engineering
The equations considered in this article have the form in which the time derivative of the unknown function is expressed as a double integral over the space variables of a weighted quadratic expression of the sought function. The domain of integration is unbounded and does not depend on time but depends on the space variable. We study the Cauchy problem in the function classes accompanying the equation with initial data on the positive half-line. In application to this problem, the convergence of the successive approximation method is justified. An estimate is given of the quality of the approximation depending on the number of the iterated solution. It is proved that, on some finite time interval, the posed Cauchy problem has at most one solution in the accompanying function class. An existence theorem is proved in the same class.