在表面生长模型中使用数值eigenvalue边界的严格后验分析
Rigorous a-posteriori analysis using numerical eigenvalue bounds in a surface growth model
摘要：
为了数值证明一类四阶非线性偏微分方程整体光滑解的存在性和唯一性，我们给出了线性化算子数值域上确界的严格后验上界.这些界限也必须易于计算，以便适用于我们严格的后验方法，因为我们在每个时间步的数值离散化中使用它们。最终目标是建立光滑局部解的全局边界，然后建立全局唯一性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
