Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation.
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Local attractivity in nonautonomous semilinear evolution equations
Joël Blot, Constantin Buşe, Philippe Cieutat (2014)
Nonautonomous Dynamical Systems
We study the local attractivity of mild solutions of equations in the form u’(t) = A(t)u(t) + f (t, u(t)), where A(t) are (possible) unbounded linear operators in a Banach space and where f is a (possible) nonlinear mapping. Under conditions of exponential stability of the linear part, we establish the local attractivity of various kinds of mild solutions. To obtain these results we provide several results on the Nemytskii operators on the space of the functions which converge to zero at infinity...
Long-term damped dynamics of the extensible suspension bridge.
Bochicchio, Ivana, Giorgi, Claudio, Vuk, Elena (2010)
International Journal of Differential Equations
Long-time behavior for 2D non-autonomous g-Navier-Stokes equations
Cung The Anh, Dao Trong Quyet (2012)
Annales Polonici Mathematici
We study the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite-dimensional pullback -attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms. Furthermore, when the force is time-independent...
Longtime behavior of semilinear reaction-diffusion equations on the whole space
Vittorino Pata, Claudio Santina (2001)
Rendiconti del Seminario Matematico della Università di Padova
Lyapunov Functions for Weak Solutions of Reaction-Diffusion Equations with Discontinuous Interaction Functions and its Applications
Mark O. Gluzman, Nataliia V. Gorban, Pavlo O. Kasyanov (2015)
Nonautonomous Dynamical Systems
In this paper we investigate additional regularity properties for global and trajectory attractors of all globally defined weak solutions of semi-linear parabolic differential reaction-diffusion equations with discontinuous nonlinearities, when initial data uτ ∈ L2(Ω). The main contributions in this paper are: (i) sufficient conditions for the existence of a Lyapunov function for all weak solutions of autonomous differential reaction-diffusion equations with discontinuous and multivalued interaction...
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