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Эта публикация цитируется в 6 научных статьях (всего в 6 статьях)
Renormalized solutions for nonlinear parabolic systems in the Lebesgue–Sobolev spaces with variable exponents
B. El Hamdaoui, J. Bennouna, A. Aberqi Université Sidi Mohammed Ben Abdellah, Morocco
Аннотация:
The existence result of renormalized solutions for a class of
nonlinear parabolic systems with variable exponents of the type
\begin{align*}
\partial_{t} e^{\lambda u_i(x,t)}& -\mathop{\mathrm{div}} (|u_i(x,t)|^{p(x)-2}u_i(x,t))\\
& +
\mathop{\mathrm{div}}(c(x,t)|u_i(x,t)|^{\gamma(x)-2}u_i(x,t))=f_{i}(x,u_{1},u_{2})-\mathop{\mathrm{div}}(F_{i}),
\end{align*}
for $i=1,2,$ is given. The nonlinearity structure changes from one
point to other in the domain $\Omega$. The source term is less
regular (bounded Radon measure) and no coercivity is in the
nondivergent lower order term
$\mathop{\mathrm{div}}(c(x,t)|u(x,t)|^{\gamma(x)-2}u(x,t))$. The main
contribution of our work is the proof of the existence of
renormalized solutions without the coercivity condition on
nonlinearities which allows us to use the Gagliardo–Nirenberg
theorem in the proof.
Ключевые слова и фразы:
parabolic problems, Lebesgue–Sobolev space, variable exponent, renormalized solutions.
Поступила в редакцию: 10.01.2016 Исправленный вариант: 06.05.2016
Образец цитирования:
B. El Hamdaoui, J. Bennouna, A. Aberqi, “Renormalized solutions for nonlinear parabolic systems in the Lebesgue–Sobolev spaces with variable exponents”, Журн. матем. физ., анал., геом., 14:1 (2018), 27–53
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag687 https://www.mathnet.ru/rus/jmag/v14/i1/p27
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Страница аннотации: | 224 | PDF полного текста: | 89 | Список литературы: | 27 |
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