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arXiv · 1712.08252

Entropy solutions for parabolic problems in Musielak framework without using the sign condition of the nonlinearities

Mohamed Saad Bouh Elemine Vall·Ahmed Ahmed·Abdelfattah Touzani·Abdelmoujib Benkirane
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Abstract

We prove in this paper the existence of solutions of nonlinear parabolic problems in inhomogeneous Musielak Orlicz Sobolev spaces, we assume neither a $\Delta_2$ nor $\nabla_2$ on the Musielak function $\varphi$. The main contribution of our work is to prove the existence of entropy solutions without the sign condition on the nonlinearity. The second term $f$ belongs to $L^1(Q)$.

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Mohamed Saad Bouh Elemine Vall, Ahmed Ahmed, Abdelfattah Touzani, Abdelmoujib Benkirane. 2017-12-21. Entropy solutions for parabolic problems in Musielak framework without using the sign condition of the nonlinearities. https://arxiv.org/abs/1712.08252

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