We consider a generalized Ostrovsky–Hunter equation and the corresponding generalized Ostrovsky one with nonlinear dispersive effects. For the first equation, we study the well-posedness of entropy solutions for the Cauchy problem. For the second equation, we prove that as the dispersion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the first one. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method.

中文翻译：

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广义Ostrovsky-Hunter方程的适定性和色散/扩散极限

我们考虑具有非线性色散效应的广义Ostrovsky-Hunter方程和相应的广义Ostrovsky方程。对于第一个方程，我们研究了柯西问题的熵解的适定性。对于第二个方程，我们证明随着色散参数趋于零，色散方程的解收敛到第一个方程的不连续弱解。证明依赖于推导合适的先验估计以及补偿紧凑性方法的应用。