The one-dimensional nonlinear heat equation with absorption: regularity of solutions and interfaces
The one-dimensional nonlinear heat equation with absorption: regularity of solutions and interfaces
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带吸收的一维非线性热方程：解和界面的正则性
DOI：
10.1137/0518011
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发表时间：
1987
影响因子：
2
通讯作者：
J. Vázquez
中科院分区：
文献类型：
--
作者：
M. Herrero;J. Vázquez
我们考虑方程$u_t = (u^m )_{xx} - \lambda u^n $与$m > 1$, $\lambda > 0$, $n \geqq m$作为热扩散与吸收的模型。因此，我们假设$u \geqq 0$代表$x \in \mathbb{R}$, $t \geqq 0$。研究了该退化抛物型方程Cauchy问题解的正则性。当初始基准面$u_0 (x)$仅在部分空间$\mathbb{R}$为正时，我们还研究了出现的自由边界的规律性。讨论了解和自由边界的渐近性质。
We consider the equation $u_t = (u^m )_{xx} - \lambda u^n $ with $m > 1$, $\lambda > 0$, $n \geqq m$ as a model for heat diffusion with absorption. Hence we assume that $u \geqq 0$ for $x \in \mathbb{R}$, $t \geqq 0$. We study the regularity of the solution to the Cauchy problem for this degenerate parabolic equation. When the initial datum $u_0 (x)$ is positive only in a part of the space $\mathbb{R}$, we also study the regularity of the free boundaries that appear. The asymptotic behavior of solutions and free boundaries is also discussed.