Дифференциальные уравнения, динамические системы и оптимальное управление

Обобщенная модель Обербека–Буссинеска с переменными коэффициентами

Р. В. Бризицкий<sup>ab

a</sup> Institute of Applied Mathematics FEB RAS, str. Radio, 7, 690041, Vladivostok, Russia
^b Far Eastern Federal University, 10 Ajax Bay, Russky Island, 690922, Vladivostok, Russia

Аннотация: The global solvability of the boundary value problem for mass transfer equations has been proven, in which the coefficients of mass expansion and reaction nonlinearly depend on the concentration of the substance, and also depend on spatial variables. The mathematical apparatus is adapted to a specific boundary value problem to prove its solvability with minimal requirements for the initial data. Additional properties of the weak solution are established and their applications are discussed.

Ключевые слова: generalized Boussinesq model, Leray–Schauder principle, maximum principle, global solvability, local uniqueness.

УДК: 517.95

MSC: 35Q35

Поступила 22 ноября 2022 г., опубликована 15 марта 2024 г.

DOI: 10.33048/semi.2024.21.015