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In this paper, we study the properties of self-similar solutions of the Cauchy problem to degenerate type double nonlinear parabolic equation with variable density and absorption. The property a FSP of solution of the Cauchy problem for a nonlinear parabolic equation is established. Based on self-similar analysis of solution the condition of Fujita type global solvability of the Cauchy problem for double nonlinear degenerate type parabolic equation with variable density is proved. The estimates for weak solution depending on grows of density, value of the numerical parameters is established. The critical cases are studied.

  • Internet havola
  • DOI
  • UzSCI tizimida yaratilgan sana 14-06-2021
  • O'qishlar soni 447
  • Nashr sanasi 20-04-2020
  • Asosiy tilIngliz
  • Sahifalar5-11
Русский

В данной работе мы изучаем свойства автомодельных решений задачи Коши для вырожденного параболического уравнения с двойной нелинейностью и с переменными плотностью и поглощением. Установлено свойство конечной скорости распространения решения задачи Коши для нелинейного параболического уравнения. На основе автомодельного анализа решения доказано условие глобальной разрешимости типа Фуджиты задачи Коши для параболического уравнения с двойной нелинейностью и с переменными плотностью и поглощением. Установлены оценки для слабого решения в зависимости от роста плотности, значения числовых параметров. Также в статье исследуются критические случаи.

English

In this paper, we study the properties of self-similar solutions of the Cauchy problem to degenerate type double nonlinear parabolic equation with variable density and absorption. The property a FSP of solution of the Cauchy problem for a nonlinear parabolic equation is established. Based on self-similar analysis of solution the condition of Fujita type global solvability of the Cauchy problem for double nonlinear degenerate type parabolic equation with variable density is proved. The estimates for weak solution depending on grows of density, value of the numerical parameters is established. The critical cases are studied.

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