Renormalized Solutions for Nonlinear Parabolic Systems in the Lebesgue{Sobolev Spaces with Variable Exponents

Автор(и)

  • B. El Hamdaoui
  • J. Bennouna Université Sidi Mohammed Ben Abdellah, Déepartement de Mathéematiques, Laboratoire LAMA, Facultée des Sciences Dhar-Mahrez, B.P 1796 Atlas Fès, Morocco
  • A. Aberqi Université Sidi Mohammed Ben Abdellah, National School of Applied Sciences, LISA, Fès, Morocco

DOI:

https://doi.org/10.15407/mag14.01.027

Ключові слова:

параболiчнi задачi, простiр Лебега-Соболєва, експонента, що змiнюється, перенормованi розв'язки.

Анотація

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.

2010:35J70, 35D05.

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Опубліковано

2018-06-20

Як цитувати

(1)
Hamdaoui, B. E.; Bennouna, J.; Aberqi, A. Renormalized Solutions for Nonlinear Parabolic Systems in the Lebesgue{Sobolev Spaces With Variable Exponents. J. Math. Phys. Anal. Geom. 2018, 14, 27-53.

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