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

2018/11/09 by Kita, Kosuke, Ôtani, Mitsuharu
#35B40 #35B45 #35K57 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.03844

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 L¹ norm characterized by the first eigenfunction of Laplacian with the Robin boundary condition.

Related

• On some parabolic systems arising from a nuclear reactor model with nonlinear boundary conditions
• Blow-up in reaction-diffusion systems under Robin boundary conditions
• Global Existence and Uniform Estimates of Solution to Reaction Diffusion\n Systems with Mass Transport Type Boundary Conditions
• Uniform boundedness for reaction-diffusion systems with mass dissipation
• Long time behavior of solutions of a reaction-diffusion equation on unbounded intervals with Robin boundary conditions