On the Existence of Solution of Some Problems for Nonlinear Loaded Parabolic Equations with Cauchy Data
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https://elib.sfu-kras.ru/handle/2311/10303Author:
Frolenkov, Igor V.
Darzhaa, Maria A.
Фроленков, Игорь В.
Даржаа, Мария А.
Date:
2014-04Abstract:
Two problems are considered in this paper. First problem is the Cauchy problem for a two-dimensional
loaded parabolic equation with coefficients dependent on unknown function and its derivatives. Second
problem is the Cauchy problem for one-dimensional equation of the Burgers-type. The sufficient condi-
tions of the existence of solutions of these problems in classes of smooth bounded functions are presented
in the paper. The method of weak approximation is used for the purpose of obtaining the proof В данной статье приведены достаточные условия существования решения в классе гладких огра-
ниченных функций задачи Коши для двумерного нагруженного параболического уравнения специ-
ального вида (коэффициенты при старших, младших членах и правой части зависят от следов
неизвестной функции и ее производных), а также получен аналогичный результат для одномер-
ного нагруженного уравнения типа Бюргерса (уравнение дополнительно содержит нелинейность
относительно решения при младшей производной по пространственной переменной) с данными
Коши. Для доказательства используется метод слабой аппроксимации
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