Quasilinear integrodifferential Bernoulli-type equations

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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.

Original languageEnglish
Article number012075
Number of pages4
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 13 Dec 2019
Event8th International Conference on Mathematical Modeling in Physical Science, IC-MSQUARE 2019 - Bratislava, Slovakia
Duration: 26 Aug 201929 Aug 2019

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