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Currently displaying 1 – 2 of 2

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Recent progress in attractors for quintic wave equations

Anton Savostianov; Sergey Zelik — 2014

Mathematica Bohemica

We report on new results concerning the global well-posedness, dissipativity and attractors for the quintic wave equations in bounded domains of $ℝ^{3}$ with damping terms of the form ${(- Δ_{x})}^{θ} \partial_{t} u$ , where $θ = 0$ or $θ = 1 / 2$ . The main ingredient of the work is the hidden extra regularity of solutions that does not follow from energy estimates. Due to the extra regularity of solutions existence of a smooth attractor then follows from the smoothing property when $θ = 1 / 2$ . For $θ = 0$ existence of smooth attractors is more complicated and follows...

Robust exponential attractors for singularly perturbed phase-field type equations.

Miranville, Alain; Zelik, Sergey — 2002

Electronic Journal of Differential Equations (EJDE) [electronic only]

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