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This article is cited in 6 scientific papers (total in 6 papers)
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
Abstract:
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.
Key words and phrases:
parabolic problems, Lebesgue–Sobolev space, variable exponent, renormalized solutions.
Received: 10.01.2016 Revised: 06.05.2016
Citation:
B. El Hamdaoui, J. Bennouna, A. Aberqi, “Renormalized solutions for nonlinear parabolic systems in the Lebesgue–Sobolev spaces with variable exponents”, Zh. Mat. Fiz. Anal. Geom., 14:1 (2018), 27–53
Linking options:
https://www.mathnet.ru/eng/jmag687 https://www.mathnet.ru/eng/jmag/v14/i1/p27
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