Vectorial quasilinear diffusion equation with dynamic boundary condition

Nakayashiki, Ryota

  • Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 211-220

Abstract

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In this paper, we consider a class of initial-boundary value problems for quasilinear PDEs, subject to the dynamic boundary conditions. Each initial-boundary problem is denoted by (S) ε with a nonnegative constant ε , and for any ε 0 , (S) ε can be regarded as a vectorial transmission system between the quasilinear equation in the spatial domain Ω , and the parabolic equation on the boundary Γ : = Ω , having a sufficient smoothness. The objective of this study is to establish a mathematical method, which can enable us to handle the transmission systems of various vectorial mathematical models, such as the Bingham type flow equations, the Ginzburg– Landau type equations, and so on. On this basis, we set the goal of this paper to prove two Main Theorems, concerned with the well-posedness of (S) ε (S) with the precise representation of solution, and ε -dependence of (S) ε , for ε 0 .

How to cite

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Nakayashiki, Ryota. "Vectorial quasilinear diffusion equation with dynamic boundary condition." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 211-220. <http://eudml.org/doc/294930>.

@inProceedings{Nakayashiki2017,
abstract = {In this paper, we consider a class of initial-boundary value problems for quasilinear PDEs, subject to the dynamic boundary conditions. Each initial-boundary problem is denoted by (S)$_\varepsilon $ with a nonnegative constant $\varepsilon $, and for any $\varepsilon \ge 0$, (S)$_\varepsilon $ can be regarded as a vectorial transmission system between the quasilinear equation in the spatial domain $\Omega $, and the parabolic equation on the boundary $\Gamma :=\partial \Omega $, having a sufficient smoothness. The objective of this study is to establish a mathematical method, which can enable us to handle the transmission systems of various vectorial mathematical models, such as the Bingham type flow equations, the Ginzburg– Landau type equations, and so on. On this basis, we set the goal of this paper to prove two Main Theorems, concerned with the well-posedness of (S)$_\varepsilon $(S) with the precise representation of solution, and $\varepsilon $-dependence of (S)$_\varepsilon $, for $\varepsilon \ge 0$.},
author = {Nakayashiki, Ryota},
booktitle = {Proceedings of Equadiff 14},
keywords = {Vectorial parabolic equation, quasilinear diffusion, dynamic boundary condition},
location = {Bratislava},
pages = {211-220},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {Vectorial quasilinear diffusion equation with dynamic boundary condition},
url = {http://eudml.org/doc/294930},
year = {2017},
}

TY - CLSWK
AU - Nakayashiki, Ryota
TI - Vectorial quasilinear diffusion equation with dynamic boundary condition
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 211
EP - 220
AB - In this paper, we consider a class of initial-boundary value problems for quasilinear PDEs, subject to the dynamic boundary conditions. Each initial-boundary problem is denoted by (S)$_\varepsilon $ with a nonnegative constant $\varepsilon $, and for any $\varepsilon \ge 0$, (S)$_\varepsilon $ can be regarded as a vectorial transmission system between the quasilinear equation in the spatial domain $\Omega $, and the parabolic equation on the boundary $\Gamma :=\partial \Omega $, having a sufficient smoothness. The objective of this study is to establish a mathematical method, which can enable us to handle the transmission systems of various vectorial mathematical models, such as the Bingham type flow equations, the Ginzburg– Landau type equations, and so on. On this basis, we set the goal of this paper to prove two Main Theorems, concerned with the well-posedness of (S)$_\varepsilon $(S) with the precise representation of solution, and $\varepsilon $-dependence of (S)$_\varepsilon $, for $\varepsilon \ge 0$.
KW - Vectorial parabolic equation, quasilinear diffusion, dynamic boundary condition
UR - http://eudml.org/doc/294930
ER -

References

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