An existence result is established for a class of quasilinear parabolic problem which is a diffusion type equations having continuous coefficients blowing up for a finite value of the unknown, a second hand \(\mu \in \mathcal {M}_{b}(Q)\) and an initial data \(u_{0}\in L^{1}(\Omega )\). We develop a technique which relies on the notion of a renormalized solution and an adequate regularization in time for certain truncation functions. Some compactness results are also shown under additional hypotheses.

中文翻译：

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具有膨胀系数和一般测度数据的非线性抛物线问题的重新归一化解

为一类拟线性抛物线问题建立了一个存在结果，该问题是一个具有连续系数的扩散型方程，对于未知数，第二手\（\ mu \ in \ mathcal {M} _ {b}（ Q）\）和初始数据在L ^ {1} \（U_ {0} \（\欧米茄）\） 。我们开发了一种技术，该技术依赖于某些截断函数的时间重新规范化解决方案和适当的正则化概念。在其他假设下还显示了一些紧凑性结果。