Bounds for global solutions of a reaction diffusion system with the Robin boundary conditions

Kosuke Kita; Mitsuharu Ôtani

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arXiv · 1811.03844

Bounds for global solutions of a reaction diffusion system with the Robin boundary conditions

Kosuke Kita·Mitsuharu Ôtani

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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 $L^1$ norm characterized by the first eigenfunction of Laplacian with the Robin boundary condition.

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Kosuke Kita, Mitsuharu Ôtani. 2018-11-09. Bounds for global solutions of a reaction diffusion system with the Robin boundary conditions. https://arxiv.org/abs/1811.03844

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