We consider two model non-linear equations describing electric oscillations in systems with distributed parameters on the basis of diodes with non-linear characteristics. We obtain equivalent integral equations for classical solutions of the Cauchy problem and the first and second initial-boundary value problems for the original equations in the half-space ##IMG## [http://ej.iop.org/images/1064-5632/84/3/449/IZV_84_3_449ieqn1.gif] {$x>0$} . Using the contraction mapping principle, we prove the local-in-time solubility of these problems. For one of these equations, we use the Pokhozhaev method of non-linear capacity to deduce a priori bounds giving rise to finite-time blow-up results and obtain upper bounds for the blow-up time. For the other, we use a modification of Levine’s method to obtain sufficient conditions for blow-up in the case of sufficiently large initial data and give a lower bound for the order of growth of a functional with the meanin...

中文翻译：

---

具有分布参数的非线性波动模型中的爆破不稳定性

我们考虑了两个模型非线性方程，它们基于具有非线性特性的二极管来描述具有分布参数的系统中的电振荡。我们获得了柯西问题的经典解的等效积分方程，以及半空间中原始方程的第一和第二初始边界值问题## IMG ## [http://ej.iop.org/images/1064 -5632 / 84/3/449 / IZV_84_3_449ieqn1.gif] {$ x> 0 $}。使用收缩映射原理，我们证明了这些问题在时间上的溶解度。对于这些方程式之一，我们使用非线性容量的Pokhozhaev方法来推导先验界限，从而产生有限时间的爆破结果并获得爆破时间的上限。对于其他，