This paper is concerned with the retarded reaction–diffusion equation ∂tu−Δu=f(u)+G(t,ut)+h(x) in a bounded domain. We allow both the nonlinear terms f and G to be supercritical, in which case the solutions may blow up in finite time, making it difficult to obtain global estimates. Here we employ some appropriate structure conditions to deal with this problem. In particular, we establish detailed global L∞-estimates and dissipative H2-estimates for the solutions and further enhance the regularity results.

中文翻译：

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延迟反应-扩散方程解的全局 [公式省略] - 估计值和耗散 [公式省略] - 估计值


本文关注有界域中的延迟反应-扩散方程 ∂tu−Δu=f（u）+G（t，ut）+h（x）。我们允许非线性项 f 和 G 都是超临界的，在这种情况下，解可能会在有限时间内爆炸，从而难以获得全局估计。在这里，我们采用一些合适的结构条件来处理这个问题。特别是，我们为解建立了详细的全局 L∞-估计和耗散 H2-估计，并进一步提高了规律性结果。