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


  • B. El Hamdaoui Université Sidi Mohammed Ben Abdellah, Département de Mathématiques, Laboratoire LAMA, Faculté des Sciences Dhar-Mahrez, B.P 1796 Atlas Fès, Morocco
  • J. Bennouna Université Sidi Mohammed Ben Abdellah, Département de Mathématiques, Laboratoire LAMA, Faculté 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


Ключові слова:

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


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.


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Як цитувати

Hamdaoui, B. E.; Bennouna, J.; Aberqi, A. Renormalized Solutions for Nonlinear Parabolic Systems in the Lebesgue-Sobolev Spaces with Variable Exponents. Журн. мат. фіз. анал. геом. 2018, 14, 27-53.





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