In this paper we introduce a matrix representation of the logarithmic wave operator and we study a second-order semilinear evolution equation governed by this operator. We present a result of local well-posedness for this problem and properties of the logarithmic wave operator in terms of the logarithmic negative Dirichlet Laplacian operator.

中文翻译：

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二阶演化方程和对数算子

在本文中，我们引入了对数波算子的矩阵表示，并研究了由该算子控制的二阶半线性演化方程。我们根据对数负 Dirichlet Laplacian 算子给出了这个问题的局部适定性结果和对数波算子的性质。