论文标题
内部hölder的连续性，用于与生物膜模型应用的多孔多孔培养基方程
Interior Hölder continuity for singular-degenerate porous medium type equations with an application to a biofilm model
论文作者
论文摘要
我们显示了一类准线性退化反应扩散方程的内部Hölder连续性。方程中的扩散系数具有多孔培养基型退化，其原始系数具有奇异性。反应项是局部界限的，除了零。我们分析的方程类别是由描述生物膜生长的模型的动机。我们的方法基于多孔介质方程的内部连续性的原始证明。我们不将自己限制为在一系列正规化问题的近似连续解决方案的弱拓扑中限制的解决方案，这是一个常见的假设。
We show interior Hölder continuity for a class of quasi-linear degenerate reaction-diffusion equations. The diffusion coefficient in the equation has a porous medium type degeneracy and its primitive has a singularity. The reaction term is locally bounded except in zero. The class of equations we analyse is motivated by a model that describes the growth of biofilms. Our method is based on the original proof of interior Hölder continuity for the porous medium equation. We do not restrict ourselves to solutions that are limits in the weak topology of a sequence of approximate continuous solutions of regularized problems, which is a common assumption.
