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Hölder continuity of interfaces for the porous medium equation with absorption. (English) Zbl 0818.35053
From the introduction: This paper is devoted to the porous medium equation with absorption $u_ t = \Delta u^ m - u^ p \quad \text{in } Q$ with $$m > 1$$ and $$p \geq 1$$, where $$Q = \mathbb{R}^ N \times (0, \infty)$$. In a recent paper, the author proved some generalized Harnack inequality for bounded weak solutions. On the basis of such kind of the Harnack inequality and its variant, we can prove the Hölder continuity of the interfaces for the solutions and this is the purpose of the present paper.

##### MSC:
 35K65 Degenerate parabolic equations 35D10 Regularity of generalized solutions of PDE (MSC2000) 76S05 Flows in porous media; filtration; seepage
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##### References:
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