Existence of periodic solutions for semilinear reaction diffusion systems
The paper deals with an autonomous reaction diffusion system of the form \[ \begin{aligned} \dot u(t,x)+\Delta u(t,x)= f(u,v)&\quad\text{in }\mathbb{R}\times\Omega,\\ \dot v(t,x)+\Delta v(t,x)= g(u,v)&\quad\text{in }\mathbb{R}\times\Omega,\\ Bu(t,x)= Bv(t, x)= 0&\quad\text{on }\mathbb{R}\times\partial\Omega, \end{aligned} \] where \(\Omega\subset \mathbb{R}^N\) \((1\leq N\leq 3)\) is a bounded domain with smooth boundary \(\partial\Omega\), \(f\), \(g\) are continuous functions: \(\mathbb{R}\times\mathbb{R}\to\mathbb{R}\) and \(B\) is a Dirichlet or Neumann type boundary operator. For certain type of functions \(f\) and \(g\) the authors are able to show the existence of periodic solutions for some periods.
scientific article; zbMATH DE number 2119147