A Note on a Damped Focusing Inhomogeneous Choquard Equation

Автор(и)

  • Lassaad Chergui Department of Mathematics, College of Science and Arts in Uglat Asugour, Qassim University, Buraydah, Kingdom of Saudia Arabia
    Preparatory Institute for Engineering Studies of Elmanar, University Campus, BP 244CP 2092, Elmanar 2, Tunis, Tunisia

DOI:

https://doi.org/10.15407/mag17.03.295

Ключові слова:

демпфоване рiвняння Шокарда, велике демпфування, глобальне iснування, розсiювання, iнварiантнi множини

Анотація

Стаття присвячена фокусувальному неоднорiдному рiвнянню Шокарда з лiнiйним демпфуванням:
$$ i\dot{u}+\triangle u+ia u=-|x|^{-\gamma}(I_{\alpha}\ast|u|^p)|u|^{p-2}u \quad \text{on} \ \mathbb R^N, $$
де $a\geq 0$ i $0<\gamma<\inf(N,2+\alpha)$. Глобальне iснування i розсiювання доведенi для вiдносно великого демпфування. Для довiльного демпфування одержано глобальне iснування, коли початковi данi належать до певних iнварiантних множин.

Mathematics Subject Classification: 35Q55

Посилання

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Chergui, L. A Note on a Damped Focusing Inhomogeneous Choquard Equation. Журн. мат. фіз. анал. геом. 2021, 17, 295-325.

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