| Title:
|
Nonlinear diffusion equations with perturbation terms on unbounded domains (English) |
| Author:
|
Kurima, Shunsuke |
| Language:
|
English |
| Journal:
|
Proceedings of Equadiff 14 |
| Volume:
|
Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017 |
| Issue:
|
2017 |
| Year:
|
|
| Pages:
|
37-44 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper considers the initial-boundary value problem for the nonlinear diffusion equation with the perturbation term $$ u_t + (-\Delta+1)\beta(u) + G(u) = g \quad \mbox{in}\ \Omega\times(0, T) $$ in an unbounded domain $\Omega \subset \mathbb{R}^N$ with smooth bounded boundary, where $N \in \mathbb{N}$, $T>0$, $\beta$, is a single-valued maximal monotone function on $\mathbb{R}$, e.g., $$ \beta(r) = |r|^{q-1}r\ (q > 0, q\neq1) $$ and $G$ is a function on $\mathbb{R}$ which can be regarded as a Lipschitz continuous operator from $(H^1(\Omega))^{*}$ to $(H^1(\Omega))^{*}$. The present work establishes existence and estimates for the above problem. (English) |
| Keyword:
|
Porous media equations, fast diffusion equations, subdifferential operators |
| MSC:
|
35K35 |
| MSC:
|
35K59 |
| MSC:
|
47H05 |
| . |
| Date available:
|
2019-09-27T09:10:52Z |
| Last updated:
|
2019-09-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/703024 |
| . |
| Reference:
|
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