Solution of the anisotropic porous medium equation in $R^n$ under an $L^1$-initial value
| dc.creator | Jian, Huaiyu | |
| dc.creator | Song, Binheng | |
| dc.date | 2006-11-29 | |
| dc.date.accessioned | 2026-07-07T07:33:29Z | |
| dc.date.available | 2026-07-07T07:33:29Z | |
| dc.description | Consider the anisotropic porous medium equation, $u_t=\sum\limits_{i=1}^n(u^{m_i})_{x_ix_i},$ where $m_i>0, (i=1,2,...,n)$ satisfying $\min\limits_{1\le i\le n}\{m_i\}\le 1,$ $\sum\limits_{i=1}^nm_i>n-2,$ and $\max\limits_{1\le i\le n}\{m_i\}\le \frac{1}{n}(2+\sum\limits_{i=1}^nm_i).$ Assuming that the initial data belong only to $L^1(\Re^n)$, we establish the existence and uniqueness of the solution for the Cauchy problem in the space, $C([0,\infty), L^1(\Re^n))\cap C(\Re^n\times(0,\infty))\cap L^\infty(\Re^n\times[ε,\infty)),$ where $ε>0$ may be arbitrary. We also show a comparison principle for such solutions. Furthermore, we prove that the solution converges to zero in the space $L^\infty(\Re^n)$ as the time goes to infinity. | |
| dc.description | 14pages | |
| dc.identifier | https://arxiv.org/abs/math/0611910 | |
| dc.identifier | http://arxiv.org/abs/math/0611910 | |
| dc.identifier | Nonlinear Analysis 64(2006) 2098-2111 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119474 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Solution of the anisotropic porous medium equation in $R^n$ under an $L^1$-initial value | |
| dc.type | text |