We establish the local (in time) solvability in the classical sense for the Cauchy problem and first and second boundary‐value problems on the half‐line for a nonlinear equation similar to Benjamin‐Bona‐Mahony‐Bürgers‐type equation. We also derive an a priori estimate that implies sufficient blow‐up conditions for the second boundary‐value problem. We obtain analytically an upper bound of the blow‐up time and refine it numerically using Richardson effective accuracy order technique.

中文翻译：

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Benjamin-Bona-Mahony-Bürgers型方程经典解的局部可解性和先验估计

对于类似于本杰明·博纳·马哈尼·伯格斯型方程的非线性方程，我们建立了柯西问题以及半线上的第一和第二边值问题的经典意义上的局部（时间）可解性。我们还得出了一个先验估计，该估计意味着第二个边值问题有足够的爆炸条件。我们通过分析得出爆破时间的上限，并使用理查森有效精度排序技术对其进行数值精炼。