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Exponential bounds and stability for a system of parabolic equations

Abstract:

In this paper we study exponential bounds and asymptotic stability of the zero solution of a non-linear system of parabolic equations with Neumann boundary conditions. First, we write the parabolic equation as an abstract ordinary differential equation in a Hilbert space. Second, we study the linear part of this ODE and find the exponential bounds. Finally, we use the variational constant formula to prove the asymptotic stability of the zero solution of this non-linear system.