Nonlinear diffusion equations with perturbation terms on unbounded domains
- Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 37-44
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topKurima, Shunsuke. "Nonlinear diffusion equations with perturbation terms on unbounded domains." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 37-44. <http://eudml.org/doc/294896>.
@inProceedings{Kurima2017,
abstract = {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., \[ \beta (r) = |r|^\{q-1\}r\ (q > 0, q\ne 1) \]
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.},
author = {Kurima, Shunsuke},
booktitle = {Proceedings of Equadiff 14},
keywords = {Porous media equations, fast diffusion equations, subdifferential operators},
location = {Bratislava},
pages = {37-44},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {Nonlinear diffusion equations with perturbation terms on unbounded domains},
url = {http://eudml.org/doc/294896},
year = {2017},
}
TY - CLSWK
AU - Kurima, Shunsuke
TI - Nonlinear diffusion equations with perturbation terms on unbounded domains
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 37
EP - 44
AB - 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., \[ \beta (r) = |r|^{q-1}r\ (q > 0, q\ne 1) \]
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.
KW - Porous media equations, fast diffusion equations, subdifferential operators
UR - http://eudml.org/doc/294896
ER -
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