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Entropy Solutions for Nonlinear Parabolic Equations with Nonstandard Growth in Non-reflexive Orlicz Spaces

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Abstract

We prove in this paper an existence result of entropy solutions for nonlinear parabolic equations of the form:

$$\begin{aligned} \displaystyle \frac{\partial u}{\partial t}-{\text {div}}\, a(x,t,u,\nabla u)-\mathrm{div}\Phi (x,t,u)= f \quad \text {in }{Q_T=\Omega \times (0,T)}, \end{aligned}$$

where the lower order term \(\Phi \) satisfies only a natural growth condition prescribed by the N-function M defining the Orlicz spaces framework and the data f are an element of \(L^1(Q_T)\). We do not assume any restriction neither on M nor on its complementary \(\overline{M}\). No particular growth is considered on \(\Phi \).

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Authors and Affiliations

  1. Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohammed Ben Abdallah University, PB 1796, Fez-Atlas, Fez, Morocco

    M. Bourahma, A. Benkirane & J. Bennouna

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  1. M. Bourahma
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  2. A. Benkirane
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  3. J. Bennouna
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Correspondence to M. Bourahma.

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Bourahma, M., Benkirane, A. & Bennouna, J. Entropy Solutions for Nonlinear Parabolic Equations with Nonstandard Growth in Non-reflexive Orlicz Spaces. Mediterr. J. Math. 18, 20 (2021). https://doi.org/10.1007/s00009-020-01668-3

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