Bounds for global solutions of a reaction diffusion system with the Robin boundary conditions
Analysis of PDEs
2018-11-12 v1
Abstract
In this paper, we consider the large-time behavior of solutions of a reaction diffusion system arising from a nuclear reactor model with the Robin boundary conditions, which consists of two real-valued unknown functions. In particular, we show that global solutions of this system are uniformly bounded in a suitable norm with respect to time. Since this system has no variational structure, we cannot apply the standard methods relying on the Lyapunov functional in order to obtain a priori estimates of global solutions. To cope with this difficulty, we make use of the weighted norm characterized by the first eigenfunction of Laplacian with the Robin boundary condition.
Keywords
Cite
@article{arxiv.1811.03844,
title = {Bounds for global solutions of a reaction diffusion system with the Robin boundary conditions},
author = {Kosuke Kita and Mitsuharu Ôtani},
journal= {arXiv preprint arXiv:1811.03844},
year = {2018}
}
Comments
15 pages