This paper is concerned with the structural stability and stabilization of solutions to the three‐component reversible Gray‐Scott system under the Dirichlet or Neumann boundary conditions defined in a bounded domain of Rn for 1  ≤  n  ≤  3. We prove that each solution depends on changes in a coefficient of the ratio of the reverse and forward reaction rates for the autocatalytic reaction as well as proving the continuous dependence on the initial data. We also prove that under Dirichlet's boundary conditions, the system is stabilized to the stationary solution by finitely many Fourier modes.

In this paper, we prove the exponential stabilization of solutions for complex Ginzburg-Landau equations using finiteparameter feedback control algorithms, which employ finitely many volume elements, Fourier modes or nodal observables (controllers). We also propose a feedback control for steering solutions of the Ginzburg-Landau equation to a desired solution of the non-controlled system. In this latter problem, the feedback controller also involves the measurement of the solution to the non-controlled system.

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Sufficient conditions of blow up in finite time of solutions to initial boundary value problems for nonlinear systems of equations of thermoelasticity type are obtained. It is shown that solutions even with large enough initial energies of the considered problems may blow up in a finite time.

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