Open AccessGlobal theorem of existence and uniqueness of the firstboundary value problem for nonlinear integrodifferential equations ofparabolic type
Author(s) -
О. П. Филатов
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-3-64-72
Subject(s) - uniqueness , mathematics , bounded function , boundary value problem , mathematical analysis , nonlinear system , norm (philosophy) , picard–lindelöf theorem , type (biology) , weak solution , initial value problem , uniqueness theorem for poisson's equation , function (biology) , fixed point theorem , physics , ecology , quantum mechanics , evolutionary biology , political science , law , biology
Global theorem of existence and uniqueness of solution of the rst boundary value problem for nonlinear integrodierential equation of parabolic type is proved. If the right-hand side of the equation is integrally bounded, then we have estimate of the norm of the dierence of two solutions, which implies continuous dependence of solution on the initial function and uniqueness of so- lution of the rst boundary value problem. The problem under consideration generalizes the real model for measuring the level of incompressible uid in the fuel tanks missiles. Therefore, such problem have a current application.