We are interested in viscous scalar conservation laws with a white-in-time but spatially correlated stochastic forcing. The equation is assumed to be one-dimensional and periodic in the space variable, and its flux function to be locally Lipschitz continuous and have at most polynomial growth. Neither the flux nor the noise need to be non-degenerate. In a first part, we show the existence and uniqueness of a global solution in a strong sense. In a second part, we establish the existence and uniqueness of an invariant measure for this strong solution.

中文翻译：

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具有随机强迫的粘性标量守恒律：强解和不变测度

我们对粘性标量守恒定律感兴趣，该规律具有白色但在时间上具有空间相关性的随机强迫。假定该方程在空间变量中是一维周期性的，其通量函数是局部Lipschitz连续的，并且最多具有多项式增长。通量和噪声都不需要保持不变。在第一部分中，我们从强烈的意义上展示了全球解决方案的存在和独特性。在第二部分中，我们为该强解建立了不变度量的存在性和唯一性。