In this paper, we investigate the existence of global attractors in Orlicz spaces for reaction–diffusion equations without upper growth restriction on nonlinearity. Firstly, we prove the well-posedness of solutions for the equations in an Orlicz space. Secondly, the existence of $(L^2\left(\Omega \right),L^{\infty }\left(\Omega \right))$-bounded absorbing sets is established. Finally, we obtain the existence of global attractors in any given Orlicz space by proving the asymptotically compactness of ${\left\{S\left(t\right)\right\}}_{t\ge 0}$ generated by the equations.

中文翻译：

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Orlicz 空间中反应扩散方程的全局吸引子

在本文中，我们研究了 Orlicz 空间中全局吸引子的存在，用于反应扩散方程，而没有非线性增长上限。首先，我们证明了Orlicz空间中方程解的适定性。其次，存在$({升}^2\left(\Omega \right),{升}^{\infty }\left(\Omega \right))$有界吸收集成立。最后，我们通过证明在任何给定的 Orlicz 空间中存在全局吸引子${\left\{秒\left(吨\right)\right\}}_{吨\ge 0}$ 由方程生成。