Bögelein Verena, Strunk Michael
Fachbereich Mathematik, Universität Salzburg, Hellbrunner Str. 34, 5020 Salzburg, Austria.
Ann Mat Pura Appl. 2024;203(2):779-804. doi: 10.1007/s10231-023-01381-4. Epub 2023 Sep 22.
In this paper, we derive a comparison principle for non-negative weak sub- and super-solutions to doubly nonlinear parabolic partial differential equations whose prototype is with and and . Instead of requiring a lower bound for the sub- or super-solutions in the whole domain , we only assume the lateral boundary data to be strictly positive. The main results yield some applications. Firstly, we obtain uniqueness of non-negative weak solutions to the associated Cauchy-Dirichlet problem. Secondly, we prove that any weak solution is also a viscosity solution.
在本文中，我们推导了一类双非线性抛物型偏微分方程非负弱下解和上解的比较原理，其原型为 以及 以及 。我们并非要求下解或上解在整个区域 中有下界，而仅假设侧向边界数据严格为正。主要结果有一些应用。首先，我们得到了相关柯西 - 狄利克雷问题非负弱解的唯一性。其次，我们证明了任何弱解也是一个粘性解。
