Questions related to “very weak” solutions of physical models of acoustic and shallow water wave propagation with singular dissipation are studied. The existence of a new type of solutions is proved. An existence theorem for a very weak solution of the problem is obtained. Finally it is shown that very weak solutions are consistent with classical ones in a certain sense, provided that the latter exist.

中文翻译：

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声学和浅水波传播与不规则耗散

研究了具有奇异耗散的声波和浅水波传播的物理模型的“非常弱”解的问题。证明了新型解决方案的存在。获得了一个非常弱的问题解决方案的存在性定理。最终表明，只要经典解存在，那么在某种意义上说非常弱的解与经典解是一致的。