Boundary-driven instability (Q1370417)

The authors show, by graphic examples, how Dirichlet boundary conditions are able to destabilize the uniform steady state of a reaction-diffusion system when the uniform steady state is stable with Neumann boundary conditions. The considered reaction diffusion system is \[ u_t= D_uu_{xx}+ (\alpha+\beta u)u-\gamma uv, \qquad v_t= D_vv_{xx}+ \delta uv-\rho v^2, \] where \(u=u(x,t)\), \(v=v(x,t)\) (in one spatial dimension), \(\alpha, \beta, \gamma, \delta, \rho\) are positive parameters, and \(D_u, D_v\) are constant diffusion coefficients.