Source-type solutions to thin-film equations in higher dimensions
Source-type solutions to thin-film equations in higher dimensions
复制标题
高维薄膜方程的源型解
DOI：
10.1017/s0956792597003197
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发表时间：
1997
影响因子：
1.9
通讯作者：
Francisco Bernis
中科院分区：
文献类型：
--
作者：
R. Ferreira;Francisco Bernis
证明了d[Ges]2的薄膜方程ht+div(hn grad(Δh))=0在0<；n<；3时存在唯一的c1源型径向自相似非负解，当n[Ges]3时没有这种类型的解.当0<；n3时，解h具有有限的传播速度，并且我们得到了h在h>；0和h=0的界面或自由边界处的一阶渐近性态.(病例d=1已知[1])。
We prove that the thin film equation ht+div (hn grad (Δh))=0 in dimension d[ges ]2 has a unique C1 source-type radial self-similar non-negative solution if 0<n<3 and has no solution of this type if n[ges ]3. When 0<n3 the solution h has finite speed of propagation and we obtain the first order asymptotic behaviour of h at the interface or free boundary separating the regions where h>0 and h=0. (The case d=1 was already known [1]).