Stability and spectral comparison of a reaction-diffusion system with mass conservation
The authors are concerned with the global in-time behavior of solutions to a reaction-diffusion system with mass conservation in the form \(u_t-D\Delta u=f(u,v)\), \(v_t=d\Delta v+g(u,v)\) subject to homogeneous Neumann boundary conditions in a smooth and bounded domain. The existence of a Lyapunov function is derived which allow the authors to deduce the existence of a global-in-time solution with compact orbit. The stability and instability of stationary solutions is next investigated by using the semi-unfolding-minimality property and the spectral comparison. Finally, the dynamics near the stationary solutions is qualitatively characterized by a variational function.
scientific article; zbMATH DE number 6921351
scientific article