Renormalized Solutions for Nonlinear Parabolic Systems in the Lebesgue-Sobolev Spaces with Variable Exponents
DOI:
https://doi.org/10.15407/mag14.01.027Анотація
Наведено результат iснування перенормованих розв'язкiв для класу нелiнiйних параболiчних систем з експонентою, що змiнюється, типу
∂teλui(x,t) - div(|ui(x, t)|p(x)-2ui(x, t))
+ div(c(x, t)|ui(x, t)|γ (x)-2ui(x, t)) = fi(x, u1, u2) - div(Fi),
для i = 1, 2. Cтруктура нелiнiйностi змiнюється вiд точки до точки в областi Ω. Член джерела менш регулярний (обмежена мiра Радона) i в недивергентному членi низшого порядку div(c(x, t)|u(x, t)|γ (x)-2u(x, t)) вiдсутня коерцитивнiсть. Основний внесок нашої роботи - це доведення iснування перенормованих розв'язкiв без умов коерцитивностi на нелiнiйностi, що дозволяє нам скористатися для доведення теоремою Гальярдо-Нiренберга.
Mathematical Subject Classification: 35J70, 35D05.
Ключові слова:
параболiчнi задачi, простiр Лебега-Соболєва, експонента, що змiнюється, перенормованi розв'язкиПосилання
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