In this paper, we are concerned with existence, uniqueness, regularity, and continuous dependence upon the initial data for mild solutions of an equation of viscoelasticity in power type materials in the \(L^q\)-setting. We also analyze the continuation of this solution up a maximal time of existence and a blow-up alternative. Finally, we obtain the global well-posedness for the problem.

中文翻译：

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$$ L ^ q $$ L q-幂型材料粘弹性方程的可解性

在本文中，我们关注在（L ^ q \）设置中幂型材料的粘弹性方程的温和解的存在性，唯一性，规则性和对初始数据的连续依赖性。我们还分析了该解决方案在最长生存时间和爆破替代方案下的持续性。最后，我们获得了该问题的全球合理性。