TY - JOUR

T1 - Quasilinear integrodifferential Bernoulli-type equations

AU - Vaskevich, V. L.

AU - Shvab, I. V.

N1 - Publisher Copyright:
© 2019 IOP Publishing Ltd.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2019/12/13

Y1 - 2019/12/13

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85077817614&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1391/1/012075

DO - 10.1088/1742-6596/1391/1/012075

M3 - Conference article

AN - SCOPUS:85077817614

VL - 1391

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012075

T2 - 8th International Conference on Mathematical Modeling in Physical Science, IC-MSQUARE 2019

Y2 - 26 August 2019 through 29 August 2019

ER -