In this article, we establish the existence of weak solutions to the shallow medium equation. We proceed by an approximation argument. First, we truncate the coefficients of the equation from above and below. Then, we prove convergence of the solutions of the truncated problem to a solution to the original equation.

中文翻译：

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扩散浅介质方程解的存在性

在本文中，我们建立了浅介质方程弱解的存在性。我们继续进行近似论证。首先，我们从上面和下面截断方程的系数。然后，我们证明截断问题的解收敛于原始方程的解。