We discuss some recent results concerning Radon measure-valued solutions of the Cauchy–Dirichlet problem for $\partial_t u = \Delta\phi(u)$. The function $\phi$ is continuous, nondecreasing, with a growth at most powerlike. Well-posedness and regularity results are described, which depend on whether the initial data charge sets of suitable capacity (determined both by the Laplacian and by the growth order of $\phi$), and on suitable compatibility conditions at $\pm\infty$.

中文翻译：

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拟线性抛物线方程的氡测值解

我们讨论了关于 $\partial_t u = \Delta\phi(u)$ 的 Cauchy-Dirichlet 问题的氡测量值解的一些最新结果。函数 $\phi$ 是连续的、非递减的，最多呈幂级增长。描述了适定性和规律性结果，这取决于初始数据电荷集是否具有合适的容量（由拉普拉斯算子和 $\phi$ 的增长顺序确定），以及 $\pm\infty 的合适兼容性条件$.