ABSTRACT

In this paper, we establish blow-up rates for a higher-order semilinear parabolic equation with nonlocal in time nonlinearity with no positive assumption on the solution. We also give Liouville-type theorem for higher-order semilinear parabolic equation with infinite memory nonlinear term which plays the main tools to prove our blow-up rate result. Finally, we study the well-posedness of mild solutions.

中文翻译：

---

具有非线性记忆项的高阶半线性抛物型方程的爆破率。

摘要

在本文中，我们建立了一个高阶半线性抛物方程的爆破率，该方程具有非局部时间非线性，而对解没有正定假设。我们还给出了具有无限记忆非线性项的高阶半线性抛物方程的Liouville型定理，它是证明爆炸率结果的主要工具。最后，我们研究温和溶液的适定性。