In order to prove numerically the global existence and uniqueness of smooth solutions of a fourth order, nonlinear PDE, we derive rigorous a-posteriori upper bounds on the supremum of the numerical range of the linearized operator. These bounds also have to be easily computable in order to be applicable to our rigorous a-posteriori methods, as we use them in each time-step of the numerical discretization. The final goal is to establish global bounds on smooth local solutions, which then establish global uniqueness.

中文翻译：

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在表面生长模型中使用特征值数值界进行严格的A后验分析

为了从数值上证明四阶非线性PDE光滑解的整体存在性和唯一性，我们在线性化算子的数值范围的最大值上得出严格的a-后验上界。这些界限还必须易于计算，以适用于我们严格的后验方法，因为我们在数值离散化的每个时间步中都使用它们。最终目标是在平滑的本地解决方案上建立全局边界，然后建立全局唯一性。