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Asymptotic selection of viscosity equilibria of semilinear evolution equations by the introduction of a slowly vanishing term

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  • The behavior at infinity is investigated of global solutions to some nonautonomous semilinear evolution equations with conservative and convex nonlinearities. It is proved that the trajectories converge to viscosity stationary solutions as time goes to infinity, that is, they evolve towards stationary solutions that are minimal with respect to a generalized viscosity criterion. Hierarchical viscosity selections and applications to specific nonlinear PDE are given.
    Mathematics Subject Classification: Primary: 35B40, 34G20; Secondary: 35K90, 37N40.

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