Dynamics of strongly damped wave equations in locally uniform spaces: Attractors and asymptotic regularity

By Meihua Yang, Chunyou Sun. 2008

48 citations recorded by the source corpus.

This paper is dedicated to analyzing the dynamical behavior of strongly damped wave equations with critical nonlinearity in locally uniform spaces. After proving the global well-posedness, we first establish the asymptotic regularity of the solutions which appears to be optimal and the existence of a bounded (in H 2 lu (R N ) x H 1 lu (R N )) subset which attracts exponentially every initial H 1 lu (R N ) x L 2 lu (R N )-bounded set with respect to the H 1 lu (R N ) x L 2 lu (R N )-norm. Then, we show there is a (H 1 lu (R N ) x L 2 lu (R N ), H 1 ρ (R N ) x H 1 ρ (R N ))-global attractor, which reflects the strongly damped property of Δu t to some extent.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/08fddeca6e8eafe7e1ef13ecb77945e2d8660de1

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In Computational Theory and Mathematics

1. Igor D. Chueshov
2. Bixiang Wang
3. Irena Lasiecka
4. A. Kh. Khanmamedov

In Control and Systems Engineering

1. Igor D. Chueshov
2. Irena Lasiecka
3. Bixiang Wang
4. A. Kh. Khanmamedov
5. Zhijian Yang

In Mathematical Physics

1. Igor D. Chueshov
2. Irena Lasiecka
3. A. Kh. Khanmamedov
4. Zhijian Yang

Citations in the corpus

• Long-time dynamics of Kirchhoff wave models with strong nonlinear damping (2010, background): “Models with different types of strong (linear) damping in wave equations were considered in [6, 7, 23, 38, 45], see also the literature quoted in these references.”