Displaying similar documents to “Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization”

On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model

Dalibor Pražák, Josef Žabenský (2013)

Open Mathematics

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We consider the so-called Ladyzhenskaya model of incompressible fluid, with an additional artificial smoothing term ɛΔ3. We establish the global existence, uniqueness, and regularity of solutions. Finally, we show that there exists an exponential attractor, whose dimension we estimate in terms of the relevant physical quantities, independently of ɛ > 0.

Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations

Albert J. Milani, Hans Volkmer (2011)

Applications of Mathematics

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We give sufficient conditions for the existence of global small solutions to the quasilinear dissipative hyperbolic equation u t t + 2 u t - a i j ( u t , ∇ u ) ∂ i ∂ j u = f corresponding to initial values and source terms of sufficiently small size, as well as of small solutions to the corresponding stationary version, i.e. the quasilinear elliptic equation - a i j ( 0 , ∇ v ) ∂ i ∂ j v = h . We then give conditions for the convergence, as t → ∞ , of the solution of the evolution equation to its stationary state.