Solvability of Strongly Nonlinear Obstacle Parabolic Problems in Inhomogeneous Orlicz–Sobolev Spaces
DOI:
https://doi.org/10.15407/mag18.04.463Анотація
У цiй роботi ми доводимо iснування розв’язкiв для нелiнiйної одно-
бiчної задачi, пов’язаної з параболiчним рiвнянням
$$
\frac{\partial u}{\partial t}- \textrm{div } a(x,t,u,\nabla u) - \textrm{div } \Phi(x,t,u) = \mu \textrm{ in } Q_T = \Omega \times (0,T),
$$
де член нижчого порядку $\Phi$ задовольняє узагальнену природну умову зростання, описану певною функцiєю Орлича $\Psi$, i функцiя µ є iнтегров-
ним членом витоку. Жодних обмежень зростання не накладається анi
на $\Psi$, анi на його спряжене $\overline{\Psi}$. Отже, розв’язок є природним у цьому
контекстi.
Mathematical Subject Classification 2010: 35K55, 35Q68, 35Q35
Ключові слова:
однобiчна параболiчна задача, нерефлексивний простiр Орлича, природне зростанняПосилання
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